Question

Using repeated subtraction method, find the HCF of the following:

1014 and 654

Answer 1

Let number be m and n

m > n

We do m – n and the result of subtraction becomes new ‘m’. if m becomes less than n, we do n – m and then assign the result as n. We should do this till m = n. When m = n then ‘m’ is the HCF.

Let m = 1014, n = 654

m – n = 1014 – 654 = 360

now m = 654, n = 360

m – n = 654 – 360 = 294

now m = 360, n = 294

m – n = 360 – 294 = 66

now m = 294 n = 66

m – n = 294 – 66 = 228

now m = 66, n = 228

n – m = 228 – 66 = 162

now m = 162, n = 66

= 162 – 66 = 96

n – m = 96 – 66 = 30

Similarly, 66 – 30 = 36

36 – 30 = 6

30 – 6 = 24

24 – 6 = 18

18 – 6 = 12

12 – 6 = 6

now m = n = 6

∴ HCF of 1014 and 654 is 6