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I think the definition of a multiple of a number is: If A is a multiple of B then it's possible to represent A as A= B* X, where X is an Integer. (A and B are also integers)

Since X must be an integer the division of A/B (X =A/B) must be an integer, otherwise A is not multiple of B.

If the division A/B is NOT an integer then A is NOT multiple of B.

Is this true?

I know that if the remainder of a number by another number is equal to 0 then they are multiple. But I'm not interested in that way to know if two numbers are multiple of each other.

Will
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    There is no general procedure that can tell you whether a number is a multiple of another number. Of course if $B=2$ or $B=5$ it can be done, but if say $B = 137$ you just have do the math (division) to see if the remainder is zero.. – M. Wind Sep 26 '21 at 15:40
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    Your claim is false: If $A$ and $B$ are both $0,,A\div B$ isn't an integer although $A$ is a multiple of $B.$ – ryang Sep 26 '21 at 16:05

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