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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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Because a number can't have a factor larger than itself.

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Q: Why is the greatest common factor of two or more integers never greater than the least of the numbers?

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

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 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.

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

Any three consecutive integers.

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

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

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 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.

The greatest common multiple of any set of integers is infinite because numbers don't stop.

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.

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.

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

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

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

Any three consecutive integers.

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

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