10. Find the HCF of the two numbers using the pr

Space for work

48 and 60

11. Solve the following in the space provided bel

69810 : 105

# 10. Find the HCF of the two numbers using the pr

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Step-by-step explanation:We will discuss here about the method of h.c.f. (highest common factor).

The highest common factor or HCF of two or more numbers is the greatest number which divides exactly the given numbers.

Let us consider two numbers 16 and 24.

Factor of 16 are → 1, 2, 4, 8, 16

Factor of 24 are → 1, 2, 3, 4, 6, 8, 12, 16

1 × 16, 2 × 8, 4 × 4

1 × 24, 2 × 12, 3 × 8, 4 × 6

We see that the highest common factor of 16 and 24 is 8. In short, the Highest Common Factor is expressed as H.C.F.

Finding H.C.F.

There are three methods of finding H.C.F. of two or more numbers.

1. Factorization Method

2. Prime Factorization Method

3. Division Method

1. H.C.F. by factorization method

Let us consider some examples.

I. Find the H.C.F. of 36 and 45.

Factor of 36 are →

1, 2, 3, 4, 6, 9, 12, 18, 36

Factor of 45 are →

1, 3, 5, 9, 15, 45

1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6

1 × 45, 3 × 15, 5 × 9

The common factors of 36 and 45 are 1, 3, 9.

The highest common factor is 9.