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Because there are many examples where that isn't so.

The GCF of 36 and 24 is 12.

The GCF of 151 and 149 is 1.

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Q: Why is it false when a pair of numbers each greater than 100 will always have a greater greatest common factor than a pair of numbers that are both less than 100?
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Related questions

Is the Greatest common factor of a pair of numbers even greater than both numbers?

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.


Is the least common multiple of two numbers always divisible by the greatest common factor of the two numbers?

Yes, the least common multiple of two numbers is always divisible by those numbers' greatest common factor.


What are the math terms gcf and LCM?

GCF - Greatest Common Factor (GCF is always smaller or equal to at least one of the numbers) LCM - Least Common Multiple (LCM is always greater or equal to at least one of the numbers)


Can the greatest common factor of positive numbers be greater than both numbers?

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


Is the Greatest Common Factor of two numbers greater than both numbers?

Yes it is.


Is the greatest common factor of two numbers always greater than 1?

No, a GCF is not always great than one. For example the GCF of 7 and 3 is 1.


Does a pair of numbers each greater than 100 always have a greater greatest common denominator than a pair of numbers that are both less than 100?

No. Although the greatest common denominator of a pair of numbers is infinite, the size of the numbers doesn't affect the GCF as much as the difference between them. The GCF of 100 and 102 is 2. The GCf of 33 and 66 is 33.


Can the greatest common factor of any set of numbers be greater than any one of the numbers?

No.


Is the greatest common factor of two different prime numbers always 1?

Yes, the greatest common factor of two different prime numbers is always 1


Is the greatest common factor of two numbers is equal to Lester of the numbers always?

No.


Is it true that when one number is multiple of another the greatest common factor of the numbers is greater of the numbers?

No, the lesser.


Why is greater common factors greater than common factors?

In any list of distinct numbers, one will be greater than the others. In the list of common factors, one will be the greatest.