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Q: When a number is a multiple of another the greatest common factor of the numbers is the greater of the numbers?

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The GCF of the numbers is the greatest common factor no matter what their relationship is. When one number is a multiple of another number, the GCF is the smaller number.

The greatest common multiple of any set of integers is infinite.

Not with negative numbers. -10 is a multiple of -2.

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.

Related questions

No, the lesser.

There is no greatest common multiples for whatever common multiple is claimed to be the greatest the lowest common multiple of the numbers (in this case 15) can be added to get an even greater common multiple.

In that scenario, the GCF is the lesser of the numbers. The LCM is the greater.

The GCF of the numbers is the greatest common factor no matter what their relationship is. When one number is a multiple of another number, the GCF is the smaller number.

There can never be a greatest common multiple of one number for two reasons:"Common" refers to a multiple that is common to two or more numbers. You cannot have a multiple that is common, but only to one number.If X is the greatest common multiple of a set of numbers, then any multiple of X will also be a common multiple of each member of the set and it will be greater than X. And then, any multiple of this number will be a multiple of each member of the set and will be greater still. And then ...

The answer is sometimes - when the multiple in question is 1.

There is no greatest common multiple of any integers as whatever number is said to be it, the lowest common multiple of the numbers can be added to get an even greater common multiple. If you mean least common multiple (the lowest (positive) integer that can be divided by the numbers without a remainder), the answer is 312. If you mean the greatest common factor (the greatest (positive) integer that can divide into the numbers without any remainder). the answer is 4.

There can be no such number. Suppose x is the least common multiple (LCM) of these numbers. Then 2*LCM is also a common multiple and is greater. And then 3*LCM is a common multiple and greater still. And so on, for ever.

The greatest common multiple of any set of integers is infinite.

There is no "greatest common multiple" of any two numbers. Whatever their product is, it can be multiplied by any positive integer to yield an even greater number that is also a multiple of the first two. Thus, the number of multiples is infinite.

The greatest common multiple of any set of numbers is infinite. The greatest common multiple of any set of numbers will never be one.

The greatest common multiple of any two numbers is infinite.

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