# Prime Factors

Prime factor is the factor of the given number which is a prime number also.

How to find the prime factors of a number?

 Let us take an example to find prime factors of 210.We need to divide 210 by the first prime number 2 we get 105. Now we need to divide 105 by the prime number 3 and we get 35. Again we need to divide 35 by the prime number 5 and we get 7. And, again we need to divide 7 by the prime number 7 and we get 1.Therefore, 210 = 2 × 3 × 5 × 7 Prime Factors of 210

In the same way if we find the factor of 14 then, they are 1, 2, 7 and 14. Out of these 2 and 7 are prime numbers.

Therefore, 2 and 7 are prime factors of 14.

Hence, 14 = 2 × 7

Some examples to find the prime factors of the given number:

(i) 15

The prime factors of 15 are 3 and 5;

15 = 3 × 5.

(ii) 21

The prime factors of 21 are 3 and 7;

21 = 3 × 7.

(iii) 30

The prime factors of 30 are 2, 3 and 5;

30 = 2 ×3 × 5.

(iv) 35

The prime factors of 35 are 5 and 7;

35 = 5× 7.

(v) 42

The prime factors of 42 are 2, 3 and 7;

42 = 2 × 3 × 7.

Questions and Answers on Prime Factors:

I. Prime numbers are building block of numbers. All composite numbers are made of prime numbers. Find how these numbers are made of prime numbers.

(i) 6 = 2 × 3

2 and 3 are both prime numbers.

(ii) 8 = 2 × 4 = 2 × 2 × 2

2 is a prime number.

(iii) 18

(iv) 15

(v) 9

(vi) 12

(vii) 21

(viii) 20

(iii) 2 × 3 × 3; 2 and 3 are both prime numbers.

(iv) 3 × 5; 3 and 5 are both prime numbers.

(v) 3 × 3; 3 is a prime number.

(vi) 2 × 2 × 3; 2 and 3 are both prime numbers.

(vii) 3 × 7; 3 and 7 are both prime numbers.

(viii) 2 × 2 × 5; 2 and 5 are both prime numbers.

II. Draw the factor tree for the given numbers to find the prime factors. First one is shown as an example for you.

(i) 24

(ii) 40

(iii) 45

(iv) 84

(v) 75

(vi) 60

(vii) 120

(viii) 144

(ix) 96

● Factors.

Common Factors.

Prime Factor.

● Repeated Prime Factors.

● Highest Common Factor (H.C.F).

● Examples on Highest Common Factor (H.C.F).

Greatest Common Factor (G.C.F).

Examples of Greatest Common Factor (G.C.F).

Prime Factorisation.

To find Highest Common Factor by using Prime Factorization Method.

Examples to find Highest Common Factor by using Prime Factorization Method.

To find Highest Common Factor by using Division Method.

Examples to find Highest Common Factor of two numbers by using Division Method.

To find the Highest Common Factor of three numbers by using Division Method.