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Why is the greatest common factor of two or more integers never greater than the least of the numbers?
Wiki User
∙ 2015-10-10 03:56:02
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.
Wiki User
∙ 2009-01-18 22:17:02
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What is the greatest common multiple of 6 and 35?
The greatest common multiple of any set of integers is infinite.
What is the greatest common multiple of 12 and 42?
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.
Can the greatest common factor be greater than 18?
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.
What is the greatest common multiple of 15 and 60?
The greatest common multiple of any set of integers is infinite.
What three numbers have a greatest common factor of 1?
Any three consecutive integers.
What is the greatest common multiple of 6 and 35?
The greatest common multiple of any set of integers is infinite.
Why can you identify the greatest common multiple between numbers?
The greatest common multiple of any set of integers is infinite.
What is the greatest common multiple of 12 and 42?
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.
Can the greatest common factor be greater than 18?
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.
What is the greatest common multiple and why?
The greatest common multiple of any set of integers is infinite because numbers don't stop.
What is the greatest common multiple of 24 and 52?
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.
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.
What is the greatest common multiple of 25 and 32?
The greatest common multiple of any set of integers is infinite.
What is the greatest common multiple of 15 and 60?
The greatest common multiple of any set of integers is infinite.
What is the greatest common multiple of 36 60?
The greatest common multiple of any set of integers is infinite.
What three numbers have a greatest common factor of 1?
Any three consecutive integers.
What is the GCM for the numbers 122430?
The greatest common multiple of any set of integers is infinite.
