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Playing With Numbers

Prime and Composite Numbers

Suppose you buy something online on Amazon or flipchart, you make use of your credit card. Here is where prime numbers come into the picture. Before your card number is sent over the wires, it is encrypted for security, and once it’s received, it is decrypted. One of the most common encryption schemes is based on prime numbers. To understand this in a better way, let us study the topic of prime numbers in detail.

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Prime and Composite Numbers
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Types of Numbers

Today let us study the two types of numbers. The two types of numbers we are going study are

  1. Prime Numbers
  2. Composite Numbers

What are Prime Numbers?

Prime Numbers

Every prime number have exactly 2 factors. Numbers having factors 1 and number itself are known as prime numbers. The prime number is the simplest of a number. Let us see few examples of prime numbers.

For example, let us take a number say 11. It can be written as 11 × 1 and 1 ×11. There is no other way of writing this number. So the factors of 11 are 1 and 11. Therefore, we can say that 11 is a prime number. Similarly, we can say for 2, 3, 5, 7, 13, 17, … etc can only be written in two forms with a single factor as 1, hence are the prime numbers.

Each prime number is only divisible by 1 and itself. That means the number 1 can never be a prime number. So any prime number should have only two factors and it should be greater than 1.

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Composite Numbers

Composite numbers are numbers which have at least one factor other than the number itself and 1. Let’s look at a few examples.

  • Let us take a number say 4. It can be written as 4 × 1, 1 ×4 and 2× 2 So the factors of 4 are 1, 2 and 4. Therefore, we can say that 4 is a composite number.
  • Now, let us take a number say 6, can be written as 6 × 1, 1 ×6,  2× 3 and 3× 2. So, the factors of 6 are 1, 2, 3 and 6. Therefore, we can say that 6 is a composite number.
  • Let us take a number say 8. It can be written as 8 × 1, 1 ×8,  2× 4 and 4× 2. So the factors of 8 are 1, 2, 4 and 8. Therefore, we can say that 8 is a composite number.

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Identify the Numbers as Prime or Composite

Let us consider the numbers from 1 to 10. Can you identify which of these numbers are prime and composite numbers?

  • Let us start with 2. We have already proved that 2 is a prime number
  • In the same way, 3 is also a prime number as 3 is divisible by only 1 and 3
  • 4 is a composite number as proved above
  • 5 is again a prime number
  • 6 is a composite number
  • 7 is a prime number
  • 8 is again a composite number
  • 9 is a composite number as it has a number of factors like 9, 1 and 3
  • 10 is also a composite number as it has multiple factors like 1, 10, 5, 2

Now, what about the number 1? The number 1 is neither prime nor a composite number.  In these way, we can identify if the number is a prime or composite number.

Solved Examples for You

Question 1: The units digit of every prime number (other than 2 and 5 ) must be necessarily

  1. 1, 3 0r 5
  2. 1, 3, 7 or 9
  3. 7 or 9
  4. 1 or 7

Solution: B is the correct option.. All the even numbers are composite so prime numbers cannot end with any of the digits 0, 2, 4, 6, 8. Therefore units digit of every prime number (other than 2 and 5) must be necessarily 1, 3, 7 0r 9.

Q. Can we say that 11 is a prime number?

A. Of course, we can say that 11 is a prime number. This is because 11 is a number that has only two distinct divisors: 1 and 11.

Q. Can we say that zero is a prime number?

A. Zero does not happen to be a prime number. Furthermore, the reason for this is that zero has more than 2 divisors. Moreover, zero is even number. Being an even number other than 2 means that it cannot be a prime number. Also, an even number can never be a prime number with the exception of number 2. 2 is the only even number that happens to be a prime number.

Q. Can we say that 41 is a prime number?

A. 41 is certainly a prime number. This because 41 is a natural number whose formation cannot take place with the multiplication of two natural numbers that are smaller than it.

Q. Can we say that 1 is a prime number?

A. 1 does not happen to be a prime number because it has only one positive divisor. This positive divisor is the number 1 itself.

 

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