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Q: Are 44 and 63 relatively prime?

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No, they are not relatively prime.

No.

No.

Yes. Their only common factor is 1.

The GCF of 21 and 44 is 1. The only proper divisors of 21 are 3 and 7. The only proper divisors of 44 are 2,4 and 11. So, could it be that there are no common factors? No! We forgot about 1 which is a divisor of every number. 1 is the only common factor of 21 and 44, so it has to be the greatest. Rule: if nothing else divides two numbers the greatest common factor is 1. We say such numbers are relatively prime to each other. 21 is relatively prime to 44 and 44 is relatively prime to 21 but neither number is prime. Exercise : Prove : If p and q are two different primes, then p and q are relatively prime.

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