# Prime Factorisation

Prime factorisation or complete factorisation of the given number is to express a given number as a product of prime factor.

For example:

1. Find prime factorisation of 36.

Prime factorisation of 36 = 2 × 2 × 3 × 3.

= 2² × 3².

[Here two ways to solve factorisation one is tree factorisation method and the other one is by dividing.]

2. Find prime factorisation of 32.

Solution:

Prime factorisation of 32 = 2 × 2 × 2 × 2 × 2.

= 2⁵.

3. Find prime factorisation of 51.

Solution:

Prime factorisation of 51 = 3 × 17.

= 3¹ × 17¹ = 3 × 17.

4. Find prime factorisation of 57.

Solution:

Prime factorisation of 57 = 3 × 19 = 3¹ × 19¹ = 3 × 19.

5. Find prime factorisation of 60.

Solution:

Prime factorisation of 60 = 2 × 2 × 3 × 5.

= 2² × 3 × 5.

6. Find prime factorisation of 63.

Solution:

Prime factorisation of 63 = 3 × 3 × 7.

= 3² × 7.

7. Find prime factorisation of 72.

Solution:

Prime factorisation of 72 = 2 × 2 × 2 × 3 × 3.

= 2³ × 3².

8. Find prime factorisation of 75.

Solution:

Prime factorisation of 75 = 3 × 5 × 5.
= 3 × 5².

9. Find prime factorisation of 78.

Solution:

Prime factorisation of 78 = 2 × 3 × 13.

10. Find prime factorisation of 93.

Solution:

Prime factorisation of 93 = 3 × 31.

11. Find prime factorisation of 102.

Solution:

Prime factorisation of 102 = 2 × 3 × 17.

12. Find prime factorisation of 120.

Solution:

Prime factorisation of 120 = 2 × 2 × 2 × 3 × 5.

= 2³ × 3 × 5.

13. Find prime factorisation of 225.

Solution:

Prime factorisation of 225 = 3 × 3 × 5 × 5.

= 3² × 5².

14. Find prime factorisation of 243.

Solution:

Prime factorisation of 243 = 3 × 3 × 3 × 3 × 3.

= 3⁵.

15. Find prime factorisation of 360.

Solution:

Prime factorisation of 360 = 2 × 2 × 2 × 3 × 3 × 5.

= 2³ × 3² × 5.

● 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.