Explain why 7 × 11 × 13 + 13 is a composite number.

Explain why $7 \times 11 \times 13 + 13$ is a composite number.

easy 2 marks Class 10 · Mathematics · Real Numbers

Answer

It equals

13 \times 78 = 1014

, which has factors other than

1

and itself, so it is composite.

The correct answer is It equals $13 \times 78 = 1014$ , which has factors other than $1$ and itself, so it is composite. — Therefore $7 \times 11 \times 13 + 13$ is composite.

Step-by-step solution

Look for a factor common to both terms. Both $7 \times 11 \times 13$ and $13$ contain $13$ .
Take $13$ out as a common factor: $7 \times 11 \times 13 + 13 = 13 \times (7 \times 11 + 1)$ .
Simplify inside the bracket: $7 \times 11 + 1 = 77 + 1 = 78$ .
So the number is $13 \times 78 = 1014$ .
A composite number is one with at least one factor other than $1$ and itself. Here both $13$ and $78$ are such factors.
Therefore $7 \times 11 \times 13 + 13$ is composite.

Common mistake: Multiplying everything out to

1014

first and then hunting for factors. Taking the common factor out immediately gives the answer in one step.

Concept tested: Composite numbers and factorisation

Published 19 August 2026 · How this solution was prepared and checked

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Explain why 7×11×13+13 is a composite number.

Step-by-step solution

Explain why $7 \times 11 \times 13 + 13$ is a composite number.