Q: Are 21 and 66 relatively prime?

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No, they are not relatively prime.

No, they are not.

Two numbers are relatively prime if the only factor they have in common is 1. Example: 12 and 17 are relatively prime because they have only 1 as a common factor. 12 and 21 are not relatively prime because they have 1 and 3 as common factors.

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.

No, they are not relatively prime.

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No, they are not relatively prime.

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No.

No, 14 and 21 are not relatively prime. They share the factor 7.No.

Yes, 4 and 21 are relatively prime. Numbers that are relatively prime only have the number 1 as a common factor. That is the case with 4 and 21.