Question

If the HCF of (a,8)=4 and (b,8)=4 then find the HCF of (a+b,8).

Answer 1

Given,

HCF of (a, 8) = 4

So, it's known that a is divisible by 4.

a ÷ 4 = k ( say)

So, a = 4k

Also,

HCF of (b, 8) = 4

So, it's known that a is divisible by 4.

b ÷ 4 = m ( say)

So, b = 4m

Now,

a + b = 4k + 4m = 4(k+m)

Now, HCF of 4(k+m), 8

Let say k+ m comes to be even,

Then k + m = 2n ( Say)

Now, HCF of 4(k+m), 8 = HCF of 4(2n), 8 = HCF of 8n, 8 is 8

Let say k+ m comes to be odd,

Then (a+b,8) is 4.

So, Finally The possible HCF of (a+b,8) is 4 or 8 depends on the whether a+b is an odd or even multiple of 4.