Prime and Composite Numbers

Jay is making goody bags for his brother's birthday. He has to fill them with candies.

He knows that everyone loves candies, so he wants to be extra careful to fill them equally.

He has a packet of 31 candies that he wants to put in smaller packets of equal number.

Jayant tries, again and again, to divide the candies up evenly, but every time, there's at least one piece leftover.

His sister tells him that it's impossible to do as 31 is a "Prime Numbers."

The number 31 can be divided by either 31 or 1. So, there will always be some candy left.

A prime number is a number that can be divided by only the number 1 and itself.

31 is a prime number because 31 ÷ 1 = 31 and 31 ÷ 31 = 1 are the only two ways we can divide 31

Let's see some more examples of prime numbers.

19 is a prime number as it is divisible by 1 and 19 only. Also, 23 is a prime number as it is divisible by 1 and 23 only.

Jay asked her sister, "So what do we call the numbers which are not prime ?"

She replied, "They are called composite numbers and these numbers can be divided into groups of equal number."

He needs to finish the goody bags! So, he decides to eat one piece of candy. Now he is left with only 30 candies.

Now he can divide 30 candies equally in different ways.

30 is a composite number because 30 is divisible by 1,2,3,5,10,15,30.

Having learnt prime numbers,let’s look at some interesting pairs of prime number forms

Now, his father gives him 35 chocolate candy while his uncle gives him 39 butterscotch candy.

Now he has to distribute both the candies in equal numbers into goody bags.

Now he again try to fill the goody bags from these candies.

He neither want to put one candy in each bag nor all candies in one bag.

He made following pairs for 35 chocolate candies 5 bags with 7 candy in each 7 bags with 5 candy in each

Similarly he made following pairs for 39 butterscotch candies 3 bags with 13 candy in each 13 bags with 3 candy in each

But he again fail to make equal number of bags.

Jayant’s sister tells him this is not possible as 39 have 1,3,13,39 as factors while 35 have 1,5,7,35 as factors.

39 and 35 don’t have any common factor except 1 that’s why you are not able to make equal bags.

His sister explained whole numbers which do not have any common factor except 1 are known as coprime numbers

She gave him more examples 21 and 22 are coprime: The factors of 21 are 1, 3, 7 and 21 The factors of 22 are 1,2,11 and 22 (the only common factor is 1)

Now he ask her sister then 5 and 7 are also coprime numbers as they dont have any common factor except 1.

She replied yes and they are special type of coprime number which are known as twin prime as difference between them is 2(7-5=2)

She gave more example 3 and 5 are also twin prime as they dont have any common factor as well as difference between them is 2(5-3=2)

Revision

A prime number is a whole number greater than 1 whose only factors are 1 and itself.

Example : 2*1=2 3*1=3 5*1=5 …………...

A composite number is a whole number that can be made by multiplying other whole numbers.

Example

When two numbers have no common factors other than 1 are known as coprime numbers.

Example : 28 and 27 are coprime: The factors of 28 are 1,2,4,7,14 and 28 The factors of 27 are 1, 3,9 and 27 (the only common factor is 1

A twin prime is a prime number that is either 2 less or 2 more than another prime number

Example

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