Question

prove that - H.C.F.(ka,kb)=k.H.C.F.(a,b)​

Answer 1

Step-by-step explanation:

For this, we need to find HCF of (ka,kb) & k*HCF of (a,b) separately.

HCF(ka,kb):

ka= k * a * 1

kb= k * b * 1

HCF= k ----------------------[1]

k*HCF(a,b):

a= 1*a

b= 1*b

As we can see a & b have no other common factor than 1, HCF= 1

k*HCF(a,b)= k * 1 = k ------------[2]

Thus, from [1] & [2],

HCF (ka,kb) = k * HCF (a,b)​

Hope it help you.