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Aditi says: 'Two numbers can be co-prime only if both of them are prime.' Which example shows she is wrong?

Class 6Playing with NumbersPlaying with Numbers
  • A16 and 21 — both composite, yet their only common factor is 1.
  • B2 and 3 — both prime, and their HCF is 1.
  • C6 and 9 — their HCF is 3.
  • D5 and 10 — one of them divides the other.

Step-by-Step Solution

16 = and share no prime at all, so their HCF is 1 and they are co-prime even though neither is prime. The trap is picking 2 and 3, which agrees with Aditi instead of contradicting her; the last two pairs are not co-prime at all.
Answer: A) 16 and 21 — both composite, yet their only common factor is 1.

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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