Answer:
Method of H.C.F.
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.
II. Find the HCF of 12, 48 and 72.
Let us first list all the factors of each number.
Factors of 12 are 1, 2, 3, 4, 6 and 12
Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72
The common factors of 12, 48 and 7 are 1, 2, 3, 4, 6 and 12.
The highest common factor is 12.
2. H.C.F. by prime factorization method
Let us consider an example.
Find the H.C.F. of 24, 36 and 48.
First we find the prime factors of 24, 36 and 48.
Method of H.C.F.
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
The common prime factors = 2, 2, 3
H.C.F. = 2 × 2 × 3 = 12
