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Assertion (A): 15 is a composite number. Reason (R): 15 has factors other than 1 and itself. Which is correct?

Class 6Playing with NumbersPlaying with Numbers
  • ABoth A and R are true, and R is the correct explanation of A.
  • BBoth A and R are true, but R is not the correct explanation of A.
  • CA is true but R is false.
  • DA is false but R is true.

Step-by-Step Solution

15 = , so it has factors 1, 3, 5, 15 — more than two factors, hence composite. R correctly explains why A is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.

Key idea: Prime vs composite

A whole number greater than 1 is **prime** if it has exactly two factors: 1 and itself. It is **composite** if it has more than two factors. The number 1 is neither prime nor composite (it has only one factor — itself). 2 is the only **even** prime; every other even number is divisible by 2 and so has at least three factors.

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