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Q: Why can a greatest common factor always be found for a set of whole numbers?

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

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

No.

No. The greatest common factor of any two or more numbers is always the single highest common factor.

No, the greatest common factor of two even numbers is not always two. For instance, the GCF of 4 and 8 is 4.

Yes.

Yes.

The greatest common factor of two numbers has to show up on the lists of factors of both numbers.

The greatest common factor of two distinct primes is always 1.

The least (meaning lowest) common factor of any set of whole numbers is always 1. The greatest common factor of any set of whole numbers will depend on the factors of the individual whole numbers in the set.

The greatest factor that two or more numbers have in common is known as the greatest common factor, or GCF.

yes

Yes.

Yes.

No.

It will always be 1.

Yes.

Yes.

Of course not. In fact, the greatest common factor of two odd numbers is never 2.-- 2 is never a factor of any odd number.-- The greatest common factor of the odd numbers 651 and 1,085 is 217.

That's the greatest common factor, or GCF.

There cannot be a greatest common factor if there are not at least two numbers to compare. The greatest common factor is the largest factor that all the numbers have in common - the largest factor that they all share.

There cannot be a greatest common factor if there are not at least two numbers to compare. The greatest common factor is the largest factor that all the numbers have in common - the largest factor that they all share.

There cannot be a greatest common factor if there are not at least two numbers to compare. The greatest common factor is the largest factor that all the numbers have in common - the largest factor that they all share.