Count the teeth on Gear A and Gear B. Which statement about the two numbers is true?

Class 6Playing with NumbersPlaying with Numbers

ABoth are not prime, so they cannot be co-prime
BThey are not co-prime, because both are even
CTheir HCF is 1, so they are co-prime
DThey are co-prime only because 9 is odd

Step-by-Step Solution

Gear A has 9 teeth (factors 1, 3, 9) and Gear B has 16 (factors 1, 2, 4, 8, 16). The only common factor is 1, so 9 and 16 are co-prime. Co-prime numbers need not be prime themselves, and 9 is not even.

Answer: C) Their HCF is 1, so they are co-prime

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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