Prime factors

Let Us Learn About Prime factors

Prime Factorization is the process of find which prime numbers you need to multiply together to get the original number. The process of find this number is called integer factorization, or prime factorization. Prime number does not have any factors apart form itself and 1, but 1 is not a prime number.

The prime numbers 30 are thus 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. A factor which is a prime number is called prime factor. All number can be expressed as a product of prime numbers.

If a number has only two different factors, 1 and itself, then the number is said to be a prime number.

For example, 31 = 1 × 31

31 is a prime number since it has only two different factors.

1= 1x1

But 1 is not a prime number since it does not have two different factors.

For example :

Factors of 14 are 1, 2, 7 and 14, out of these 2 and 7 are prime numbers; thus, 2 and 7 are prime factors of 14.

Also, 14 = 2x7

In the same way :

(i)Prime factors of 15 are 3 and 5; and 15 = 3x5 [here we need to break each given numbers i.e. 15 into its prime factor 3 and 5]

(ii)Prime factors of 42 are 2, 3 and 7; and 42 = 2x3x7 [here we need to break each given numbers into its prime factor]

(iii)Prime factors of 10 are 2 and 5; and 10 = 2x5 [here we need to break each given numbers into its prime factor]

Repeated Prime Factor :

Since, 8 = 2 x 2 x 2; 2 is said to be repeated prime factor of 8.

A number can have two or more different repeated prime factors.

(i)36 = 2 x 2 x 3 x 3[here we can observe that in the factor of 36 two different repeated prime numbers 2 and 3]

Therefore, the prime factors of 36 are 2,2,3 and 3.

(ii)108 = 2 x 2 x 3 x 3 x 3 [here we can observe that in the factor of 108 two different repeated prime numbers 2 and 3]

Therefore, the prime factors of 108 are 2,2,3,3 and 3.

(iii)225 = 3 x 3 x 5 x 5 [here we can observe that in the factor of 225 two different repeated prime numbers 3 and 5]

Therefore, the prime factors of 225 are 3,3,5 and 5.

(iv)100 = 2 x 2 x 5 x 5 [here we can observe that in the factor of 100 two different repeated prime numbers 2 and 5]

Therefore, the prime factors of 100 are 2,2,5 and 5.

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