📚 CBSE Grade-10 Study Guide Open in the Study Guide single page app →
HomeMathematics

Mathematics — CBSE Class 10 board question

Q1. [1]
If $p$ and $q$ are natural numbers and $p$ is a multiple of $q$, then what is the HCF of $p$ and $q$?
  1. (a) $pq$
  2. (b) $p$
  3. (c) $q$
  4. (d) $p + q$
Previously asked in CBSE board exam
2023 30/2/1 Q4
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding rag
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.

If a question refers to an image, map, graph or diagram that is not shown here, open the Study Guide single page app, go to Library and find the actual CBSE question paper. The original papers are also available on the CBSE website: cbse.gov.in.
Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.