Natural Numbers

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

The set of natural numbers is denoted by N.

Number line
Example 1:
Example 2:

Prime numbers and Composite numbers


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.


Example


  •  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).

Note:

  •  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 and composite number 1-100 chart

*Prime numbers – blue squares

*Composite numbers – white squares

*1 is neither a prime nor a composite number.


Example 1:
  Prime numbers are 11, 13, 17, 19
Composite numbers are 12, 14,15, 16, 18

Explanation:

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.


Prime numbers and Composite numbers


Basic Examples :
  It is a composite number

Explanation:

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).


  It is a composite number

Explanation:

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


  No

Explanation:

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


  Composite

Explanation:

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.


Twin primes


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


Examples :

(3, 5)

(11, 13)


  Yes

Explanation:

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


  Yes

Explanation:

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


Co-prime and relative prime numbers


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.


Examples :
  Yes

Explanation:

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.


  Yes

Explanation:

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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