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

It equals 13 × 78 = 1014, which has factors other than 1 and itself, so it is composite. Look for a factor common to both terms. Both 7 × 11 × 13 and 13 contain 13. Take 13 out as a common factor: 7 × 11 × 13 + 13 = 13 × (7 × 11 + 1). Simplify inside the bracket: 7 × 11 + 1 = 77 + 1 = 78. So the number is 13 × 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 × 11 × 13 + 13 is composite.

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.

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

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

Step-by-step solution

Related questions

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