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I think you meant to say that it's never greater than the least of the numbers.

The easiest explanation is to simply remind you that the GCF is a factor of every number

in the group, and no factor of a number can be greater than the number itself.

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11y ago
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8y ago

A factor can't be greater than a number it's compared to.

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Q: Why GCF of two or more positive integers never greater than the least of the numbers?
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Related questions

When putting integers into greatest to least what comes first negative or positive?

Negative numbers are smaller than 0, while positive numbers are greater than zero. Therefore, when ordering integers from greatest to least, positive numbers come first. Here is an example of a list of integers ordered from greatest to least: 99, 54, 26, 21, 14, 8, 2, -5, -14, -62, -87, -89, -92, -98


Why is 1 the least positive integer?

Integers are numbers that are not followed by decimals, so they are "complete" numbers. Numbers below zero are not positive, and zero itself is neither positive nor negative, so positive integers are 1, 2, 3, 4, 5, and so on. 1 is the smallest number of these, so it is the least positive integer.


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Actually, the "set of whole numbers" doesn't have a unique definition, so it's better to avoid that term, at least in professional circles. For some people, "whole numbers" means positive numbers (usually including zero), for others, it means "integers" (i.e., both positive and negative whole numbers). The only thing you can be sure about when the term "whole numbers" is used is that it does NOT include fractions or numbers with decimals. The term "natural numbers", on the other hand, was originally used for whole numbers starting with 1; but in recent decades, it has become quite common to include zero. To avoid confusion, you better use terms such as: "Positive integers" (greater or equal to 1) "Non-negative integers" (greater or equal to 0) "Integers" (any whole number, can be zero, positive, negative).


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Does the set of a whole number includes zero but the natural number do not?

Actually, the "set of whole numbers" doesn't have a unique definition, so it's better to avoid that term, at least in professional circles. For some people, "whole numbers" means positive numbers (usually including zero), for others, it means "integers" (i.e., both positive and negative whole numbers). The only thing you can be sure about when the term "whole numbers" is used is that it does NOT include fractions or numbers with decimals. The term "natural numbers", on the other hand, was originally used for whole numbers starting with 1; but in recent decades, it has become quite common to include zero. To avoid confusion, you better use terms such as: "Positive integers" (greater or equal to 1) "Non-negative integers" (greater or equal to 0) "Integers" (any whole number, can be zero, positive, negative).


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