# Prime and Composite Numbers

## Grade 5 : Prime and Composite Numbers

Que : What are the prime and composite numbers?

## Prime Numbers:

Prime numbers are those numbers which have only two factors 1 and the number itself.

In other words, a number which is divisible by only itself and 1 is a prime number. So, prime number has only two different factors 1 and the number itself.

For example,

These numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, etc which have only two factors i.e. 1 and the number itself.

## Twin Primes:

If the difference between the two prime numbers is 2 they are called twin primes. For example (3, 5), (5, 7) and (11, 13) are set of twin primes.

So, two consecutive prime numbers having only one number between them are called twin primes.

In other words,

If two prime numbers can be paired with a difference of 2, that is they have one composite number between them, then the pair is called a twin prime.

For example; (3, 5), (5, 7), (11, 13), (17, 19), (41, 43), (59, 61), (71, 73), etc.

## Co-Prime Numbers:

If two numbers have only 1 as a common factor, they are called as co-primes. For example (2, 3), (4, 5), (3, 7) and (4, 9) are co-primes.

## Composite Numbers:

Composite numbers are those numbers which have more than two factors.

In other words, a number that has more than two different factors is a composite number. So, a composite number is also exactly divisible by numbers other than 1 and itself.

For example,

4 is a composite number and it can be divided by 1, 2 and 4.

6 is a composite number and it can be divided by 1, 2, 3 and 6.

8 is a composite number and it can be divided by 1, 2, 4 and 8.

9 is a composite number and it can be divided by 1, 3 and 9.

Therefore, 1 is a unique number that is neither prime nor composite as it has only one factor.

Observe the following table.

The numbers 2, 3, 5, ……. have only 2 factors, 1 and itself.

Such numbers are called Prime numbers.

The numbers 4, 6, …… have more than 2 factors.

Such numbers are called Composite numbers.

Note:

(i) 1 is neither a prime nor a composite number.

(ii) 2 is the smallest prime number.

(iii) 2 is the only even prime number.

(iv) No prime number ends with zero or 5.

A prime number is a natural number which has only two different factors, 1 and the number itself. A composite number is a natural number which has more than two different factors.

## Prime Numbers Between 1 and 100

The Sieve of Eratosthenes: This is a simple method to find out the prime numbers. This method was invented by a Greek astronomer Eratosthenes about 230 B.C.

Let us find all the prime numbers between 1 and 100.

Steps:

(i) 1 is not a prime number. Cross it.

(ii) 2 is a prime number. Circle 2 and cross out all the multiples of 2.

(iii) The next prime number is 3. Circle 3 and cross out all the multiples of 3.

(iv) The next prime number is 5. Circle 5 and cross out all the multiples of 5.

(v) The next prime number is 7. Circle 7 and cross out all the multiples of 73.

(vi) The next prime number is 11. Circle 11 and cross out all the multiples of 11.

(vii) The next prime number is 13. Circle 13 and cross out all the multiples of 13.

(viii) The next prime number is 17. Circle 17 and cross out all the multiples of 17.

(ix) The next prime number is 19. Circle 19 and cross out all the multiples of 19.

(x) The next prime number is 23. Circle 23 and cross out all the multiples of 23.

(xi) Continue the process till all the numbers are either circled or cross out.

## Solved Example on Prime and Composite Numbers:

Identify prime numbers and composite numbers in the given numbers 3, 8, 17, 23, 25, 32, 41, 44.

3 = 3 × 1, factor of 3 are 3 and 1.

8 = 1 × 8, 8 = 2 × 4, factor of 8 are 1, 2, 4 and 8.

17 = 1 × 17, factor of 17 are 1 and 17.

23 = 1 × 23, factor of 23 are 1 and 23.

25 = 1 × 25, 25 = 5 × 5, factor of 25 are 1, 5 and 25.

32 = 1 × 32, 32 = 2 × 16, 32 = 4 × 8, factor of 32 are 1, 2, 4, 8, 16 and 32.

41 = 1 × 41, factor of 41 are 1 and 41.

44 = 1 × 44, 44 = 2 × 22, 44 = 4 × 11, factor of 44 are 1, 2, 4, 11, 22 and 44.

The numbers having only two factors are 3, 17, 23 and 41. Therefore, 3, 17, 23 and 41 are prime numbers. Composite numbers are 8, 25, 32, 36 and 44.

Thanks…