If $p$ and $q$ are natural numbers and $p$ is a multiple of $q$, then what is the HCF of $p$ and $q$?

Question

Accepted Answer

## Model Answer **(c) $q$** Since $p$ is a multiple of $q$, we have $p = kq$ for some natural number $k$. Thus $q$ divides $p$, making $q$ the highest common factor. So HCF$(p, q) = q$. ## Explanation When one number is a multiple of the other, the smaller number ($q$) is always the HCF, because $q$ divides both itself and $p$ completely. The largest such divisor is $q$ itself.

Mathematics — Standard (041) — CBSE Class 10 board question