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Q: Do all composite numbers share the greatest common factor that is greater than 1?

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No. Two composite numbers, like 4 and 9, can have a GCF of 1. They are said to be relatively prime or co-prime.

Not necessarily.

The Greatest Common Factor depends upon the numbers for which there are common factors and it is the greatest one of them; it can be greater than 18, for example the greatest common factor of 40 and 100 is 20. The greatest common factor must be one of the factors of each of the numbers. As the factors of each number cannot be greater than that number, the greatest common factor of a set of numbers cannot be greater than the least number. If this number is not greater than 18 then the greatest common factor of the numbers cannot be greater than 18. Even if the least number is greater than 18 it is possible that the greatest common factor of a set of numbers is still not greater than 18, for example the greatest common factor of 20, 30 and 50 is 10.

4 and 9

25 and 36

15 and 16

8 and 16

Yes.

No, the greatest common factor is never greater than the smallest number. The greatest common factor is the largest integer that divides evenly into all of the numbers listed.

No.

Yes it is.

24, 25 and 26

8 and 16

25, 36, 49

8 and 16

Composite. All whole numbers ending in zero are composite.

No, the greatest common factor cannot be larger than any of the numbers in the set.

When they have a factor in common greater than one.

No, the GCF is the lesser of the numbers.

No.

8 and 16, among others.

25 and 32

No, the lesser.

If the GCF of two composite numbers is 1, they are co-prime or relatively prime.