# Composite and Prime numbers

Composite and prime numbers are the numbers whose factors are either 1 and number itself or more than two factors.There are numbers who have exactly two factors – 1 and the number itself. These numbers are known as Prime Numbers. These numbers are 2, 3, 5, 7, 11 etc.

There are other numbers which have more than two factors. These numbers are known as composite numbers. These numbers are 4, 6, 8, 9, 10, and 20 and so on.

**1 is neither a prime nor a composite number.**

In order to find whether a number is a prime number or a composite number, we need to factorize the given number.

**Solved example:-**

Check if 48 is a composite number or a prime number.

48

= 12 x 4

= 3 x 4 x 4

= 3 x 2 x 2 x 2 x 2

48 has more than two factors.

Hence, we can see that 48 is a composite number as it has more than two factors.

If we do not want to factorize each and every number in order to see whether it is a prime number or a composite number, we can find the prime numbers from 1 to 100 with an easier method.

Step 1: cross out 1 as it is not a prime number.

Step 2: encircle 2 and cross out all the multiples of 2.

Step 3: go to number 3 and encircle it and repeat the method that we did with number 2, i.e. cross out all the multiples of 3.

Step 4: repeat the steps given in step 2 and step 3 with the remaining numbers

Result: The encircled numbers are the prime numbers and the crossed out numbers are the composite numbers.

This method was given by Greek mathematician Eratosthenes in third century B.C. This method is known as the Sieve of Eratosthenes.

## Practice Questions on Composite and Prime numbers

Solve the following questions using factorization method.1. Check whether 27 is a prime number or a composite number.

2. Check whether 8 is a prime number or a composite number.

3. Check whether 99 is a prime number or a composite number.

4. Write all the prime numbers less than 20.

5. Write the greatest prime number between 10 to 20.

6. Give two pairs of the prime numbers whose difference is 2.What are they?

7. Check whether 51 is a prime number or a composite number.

8. Write five consecutive prime numbers less than 50.

9. Check whether 47 is a prime number or a composite number.If prime/composite then why?

10. Check whether 17 is a prime number or a composite number.

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