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NCERT Solutions for Class 6 Maths Chapter 3

Exercises

161 Qs

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Find the possible factors of , and .

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Write all the factors of the following number.
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Write all the factors of the following numbers.
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Write all the factors of the following number.
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Write all the factors of the following number.
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Write all the factors of the following number.
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Write all the factors of the following number.
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Write all the factors of the following number.
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Write all the factors of the following number.
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Write all the factors of the following number.
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Write first five multiples of .

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Write first five multiples of .

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Write first five multiples of .

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Match the items in column with the items in column .

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Find all the multiples of upto .

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Observe that is a prime number. Here, has been added to a multiple of to get a prime number. Can you find some more numbers of this type?

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What is the sum of any two odd numbers?

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What is the sum of any two Even numbers?

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State whether the following statement is True or False.
The sum of three odd numbers is even.

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State whether the following statement is True or False.
The sum of two odd numbers and one even number is even.

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State whether the following statement is True or False.
The product of three odd numbers is odd.

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State whether the following statement is True or False.
If an even number is divided by , the quotient is always odd.

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State whether the following statement is True or False.
All prime numbers are odd.

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State whether the following statement is True or False.
Prime numbers do not have any factors.

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State whether the following statement is True or False.
Sum of two prime numbers is always even.

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State whether the following statement is True or False.
is the only even prime number.

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State whether the following statement is True or False.
All even numbers are composite numbers.

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State whether the following statement is True or False.
The product of two even numbers is always even.

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The numbers and are prime numbers. Both these numbers have same digits and . Find such pairs of prime numbers upto .

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Write down separately the prime and composite numbers less than .

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What is the greatest prime number between and ?

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Express the following as the sum of two odd primes.
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Express the following as the sum of two odd primes.
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Express the following as the sum of two odd primes.
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Express the following as the sum of two odd primes.
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Give three pairs of prime numbers whose difference is . [Remark: Two prime numbers whose difference is are called twin primes].

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Which of the following numbers are prime?
(a)
(b)
(c)
(d) .

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Write seven consecutive composite numbers less than so that there is no prime number between them.

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Express the following number as the sum of three odd primes.
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Express the following number as the sum of three odd primes.
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Express the following number as the sum of three odd primes.
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Express the following number as the sum of three odd prime.
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Write five pairs of prime numbers less than whose sum is divisibly by .

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Fill in the blank.
A number which has only two factors is called a _______.

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Fill in the blanks.
A number which has more than two factors is called a _______.

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Fill in the blanks.
is neither __________ nor _________.

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Fill in the blank.
The smallest prime number is _______.

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Fill in the blank.
The smallest composite number is _______.

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Fill in the blank.
The smallest even number is ________.

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 Number Divisible by
 2 4 6 8 9 1011 
 128 Yes No Yes No No Yes No No No
 990 ... ... ... ... ... ... ...... ... 
 1586 ......  ... ......  ......  ... ...
 275 ... ... ...... ... ... ...  ... ...
 6686 ... ... ... ... ... ... ......  ...
 639210 ... ... ... ... ... ... ... ... ...
 429714 ... ... ... ... ... ... ... ... ...
 2856 ... ... ... ... ... ... ... ... ...
 3060 ... ... ......  ... ... ... ... ...
 406839...  ... ... ... ... ... ... ... ...
Using divisibility tests, determine which of the following numbers are divisible by ; by ; by ; by ; by ; by ; by ; by ; by (say, yes or no).

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Using divisibility tests, determine the following number is divisible by , by .
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Using divisibility tests, determine the following number is divisible by ; by .
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Using divisibility tests, determine the following number is divisible by ; by .
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Using divisibility tests, determine the following number is divisible by ; by .
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Using divisibility tests, determine the following number is divisible by ; by .
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Using divisibility tests, determine the following number is divisible by ; by .
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Using divisibility tests, determine the following number is divisible by ; by .
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Using divisibility tests, determine the following number is divisible by ; by .
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Using divisibility tests, determine the following number is divisible by ; by .
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Using divisibility tests, determine the following number is divisible by ; by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility test, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility test, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Using divisibility tests, determine the following number is divisible by .
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Write a digit in the blank space of the following number so that the number formed is divisible by .
____.

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Write a digit in the blank space of the following number so that the number formed is divisible by .
___.

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Write the smallest digit and the greatest digit in the blank space of the following number formed is divisible by .
_.

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Write the smallest digit and the greatest digit in the blank space of the following number so that the number formed is divisible by .
_.

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Find the common factors of .

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Find the common factors of .

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Find the common factors of and .

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Find the common factors of and .

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Find the common factors of and .

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Find the common factors of and .

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Find the common factors of and .

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Find the common factors of and .

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Find first three common multiples of and .

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Find first three common multiples of and .

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Write all the numbers less than which are common multiples of and .

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Determine the following numbers are co-prime.
and .

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Determine the following numbers are co-prime.
and .

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Determine the following numbers are co-prime.
and .

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Determine the following numbers are co-prime.
and .

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Determine the numbers are co-prime?
and .

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Determine the following numbers are co-prime.
and .

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A number is divisible by both and . By which other number will that number be always divisible?

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A number is divisible by . By what other numbers will that number be divisible?

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Write the prime factorisations of .

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State whether the following statement is true or false.
If a number is divisible by , it must be divisible by .

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State whether the following statement is true or false.
If a number is divisible by , it must be divisible by .

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State whether the following statement is True or False.
A number is divisible by , if it is divisible by both and .

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State whether the following statement is True or False.
If a number is divisible by and both, then it must be divisible by .

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State whether the following statement is True or False.
If two numbers are co-primes, at least one of them must be prime.

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State whether the following statement is True or False.
All numbers which are divisible by must also be divisible by .

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State whether the following statement is True or False.
All numbers which are divisible by must also be divisible by .

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State whether the following statement is True or False.
If a number exactly divides two numbers separately, it must exactly divide their sum.

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State whether the following statement is True or False.
If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

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Here is factor tree for . Write the missing number.

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Here is factor tree for . Write the missing numbers.

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Which factors are not included in the prime factorisation of a composite number?

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Write the greatest -digit number and express it in terms of its prime factors.

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Write the smallest -digit number and express it in the form of its prime factors.

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Find all the prime factors of and arrange them in ascending order. Now state the relation, if any; between two consecutive prime factors.

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The product of three consecutive numbers is always divisible by . Verify this statement with the help of some examples.

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The sum of two consecutive odd numbers is divisible by . Verify this statement with the help of some examples.

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In the following expressions, prime factorisation has been done?
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In the following expression, prime factorisation has been done?
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In the following expression, prime factorisation has been done?
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In the following expression, prime factorisation has been done?
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Determine if is divisible by .

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is divisible by both and . It is also divisible by . Similarly, a number is divisible by both and . Can we say that the number must also be divisible by ? If not, give an example to justify your answer.

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I am the smallest number, having four different prime factors. Can you find me?

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Find the HCF of the following
and .

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Find the HCF of the following.
and .

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Find the HCF of the following.
and .

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Find the HCF of the following.
and .

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Find the HCF of the following numbers.
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Find the HCF of the following number.
, .

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Find the HCF of the following number.
, .

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Find the HCF of the following numbers.
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Find the HCF of the following numbers.
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Find the HCF of the following numbers.
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Find the HCF of the following numbers.
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Find the HCF of the following numbers.
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Find the HCF of the following numbers.
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Find the HCF of the following numbers.
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What is the HCF of two consecutive numbers?

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What is the HCF of two consecutive even numbers?

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What is the HCF of two consecutive odd numbers?

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What is the HCF of two consecutive even numbers?

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What is the HCF of two consecutive even numbers?

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HCF of co-prime numbers and was found as follows by factorisation: and since there is no common prime factor, so HCF of and is . Is the answer correct? If not, what is the correct HCF?

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Renu purchases two bags of fertiliser of weights kg and kg. Find the maximum value of weight which can measure the weight of the fertiliser exact number of times.

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Three boys step off together from the same spot. Their steps measure cm, cm and cm respectively. What is the minimum distance each should cover so that all can cover the distance in complete steps?

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The length, breadth and height of a room are cm, cm and cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.

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Determine the smallest -digit number which is exactly divisible by and .

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Determine the greatest -digit number exactly divisible by , and .

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The traffic lights at three different road crossings change after every seconds, seconds and seconds respectively. If they change simultaneously at a.m., at what time will they change simultaneously again?

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Three tankers contain litres, litres and litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of the three containers exact number of times.

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Find the least number which when divided by , and leave remainder in each case.

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Find the smallest -digit number which is divisible by and .

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Find the LCM of the following numbers.
and
Observe a common property in the obtained LCMs. Is LCM the product of two numbers?

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Find the LCM of the following numbers.
and
Observe a common property in the obtained LCMs. Is LCM the product of two numbers?

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Find the LCM of the following numbers.
and .
Observe a common property in the obtained LCMs. Is LCM the product of two numbers?

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Find the LCM of the following numbers.
and
Observe a common properly in the obtained LCMs. Is LCM the product of two numbers?

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Find the LCM of the following numbers in which one number is the factor of the other.

What do you observe in the results obtained?

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Find the LCM of the following numbers in which one number is the factor of the other.

What do you observe in the results obtained?

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Find the LCM of the following numbers in which one number is the factor of the other.

What do you observe in the results obtained?

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Find the LCM of the following numbers in which one number is the factor of the other.

What do you observe in the results obtained?

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