Page 37 - Math 7

Operations on Whole Numbers

3.2 Highest Common Factor (H. C. F.)

Let’s take F and F are the sets of all possible factors of 12 and 18 respectively.
12
18
Here, F = { 1, 2, 3, 4, 6, 12 } and F = { 1, 2, 3, 6, 9, 18}
12 18
Now, let’s make another set of the common factors of F and F .
12 18
F ˆ F = { 1, 2, 3, 6}
18
12
Among these common factors, 6 is the highest one. So, 6 is called the Highest
Common Factor (H.C.F) of 12 and 18.
Let's remember the following steps to find H. C. F. from all possible factors of the
given numbers.
Step 1: Find all possible factors of given numbers.
Step 2: List the factors common to the given number.

Step 3: Write the highest/greatest one as H.C.F.
3.3 Finding H. C. F. by Factorization Method
In this method, we should find the prime factors of the given numbers. Then,
the product of the common prime factors is the H.C.F. of the given numbers. For
example:

Find the H.C.F. of 24 and 36.
Finding the prime factors of 24 and 36.
2 24 2 36
2 12 2 18 Here, 24 = 2 × 2 × 2 × 3
2 6 3 9 36 = 2 × 2 × 3 × 3 H.C.F. = Product of common
3 3 ? HCF = 2 × 2 × 3 = 12 prime factors
2
3.4 Finding H.C.F. by Division Method
In this method, we divide the larger number by the smaller one. Again, the first
remainder so obtained divides the first divisor. The process is continued till the
remainder becomes zero. The last divisor for which the remainder becomes zero is
the H.C.F. of the given numbers. For example:

Find the H.C.F. of 28 and 48.
Dividing the greater number
28) 48 (1 by the smaller one.
–28
20) 28 (1 Since the remainder is not zero, dividing
st
–20 the 1 divisor 28 by the remainder 20.
8) 20 (2 Since, the remainder is not zero, dividing
–16 divisor 20 by the remainder 8.
4) 8 (2 Since, the remainder is not zero, dividing
–8 the divisor 8 by the remainder 4.
? H.C.F. = 4 0 Since, the remainder is zero for the divisor 4,
the H.C.F. is 4.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 35 Vedanta Excel in Mathematics - Book 7