Natural numbers are whole, non-negative numbers that are used for counting objects.

The set of natural numbers is denoted by N.

A **prime number** is a natural number greater by 1, and which can be divided evenly by 1 or itself.

A **composite number** is a whole number that can be divided evenly by numbers other than 1 or itself.

- 3 is a prime number because 3 can be divided only by 1 and 3 (without any remainder)
- 6 can be divided by 1, 2, 3 and 6, so it is not a prime number (it is a composite number).

- 0 and 1 are neither prime nor composite numbers
- Composite number is a natural number that can be divided by 1, itself or by other positive numbers.

The table below shows the prime and composite numbers from 1 to 100.

*Prime numbers – blue squares

*Composite numbers – white squares

*1 is neither a prime nor a composite number.

Composite numbers are 12, 14,15, 16, 18

11, 13, 15, 17, 19 can be divided evenly by 1 or the number itself hence they are prime numbers.

12 can be divided evenly by 1, 2, 3 and 12

14 can be divided evenly by 1, 7 and 14

16 can be divided evenly by 1, 2, 4, 8 and 16

18 can be divided evenly by 1, 2, 3, 6, 9 and 18

So, they are composite numbers.

To find whether a number is prime or composite,

1. Find all the factors of the number

2. If the number has only two factors - 1 and itself, then it is prime.

3. If the number has more than two factors, then it is composite in nature.

So, going by the above rule, 2478 is a composite number because it has more than two factors and it can be divided evenly (by 2).

55 is a composite number because it has more than two factors and it can be divided evenly (by 5).

When you add the digits in 2475, the result is 18

2+4+7+5= 18

18 is not divisible by 11

Hence,

2475 is not divisible by 11

217 is an odd number so it's not divisible by 2.

.Next, test for divisibility by 3, and for that, add the digits

2 + 1 + 7 = 10.

Since 10 is not a multiple of 3, 217 is not divisible by 3.

When you add the digits in 217, it doesn't give 0 or 5 so it is not divisible by 5.

Next, test for divisibility by 7.

We can evenly divide 217 by 7 (217÷7=31)

So, 217 is a composite number.

A twin prime is a pair of prime numbers that differ by two.

(3, 5)

(11, 13)

197 and 199 are prime numbers, and there is difference of two between these numbers. So, 197 and 199 is a twin prime.

599 and 601 are prime numbers, and there is difference of two between these numbers. So, 599 and 601 is a twin prime.

Two integers are relative prime or co-prime if the only positive integer that evenly divides both of them is 1 (that is, their greatest common divisor is one).

**Example**

Let us consider the divisors of the numbers 18 and 23.

Divisors of 18: 1, 2, 3, 6, 9, 18

Divisors of 23: 1, 23

The only common number in these two sets of divisors is 1.

So, 18 and 23 are co-primes.

Divisors of 3: 1, 3

Divisors of 8: 1, 2, 4

The only common number in these two sets of divisors is 1.

So, 3 and 8 are co-primes.

Divisors of 21: 1, 3,7, 21

Divisors of 22: 1, 2,11, 22

The only common number in these two sets of divisors is 1.

So, 21 and 22 are co-primes.

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