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Q: When is the greatest common factor of two numbers less than both numbers but greater than 1?

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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.

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, the greatest common factor cannot be larger than any of the numbers in the set.

No.

Yes it is.

The greatest common factor of 2, 8, and 14 is 2. The greatest common factor of any set of numbers can't be greater than the smallest of the numbers.

No, the GCF is the lesser of the numbers.

No.

Factor both numbers. Select the factors they both have in common. Choose the largest (greatest) one.

No, the lesser.

No.

A common factor of two numbers is a factor of both numbers. The largest factor that a number has is itself, so the greatest factor that the smaller number can have is itself. If it is a factor of the larger number then it would be the greatest common factor. If not , the greatest common factor would have to be smaller.

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