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I found this on another forum

Question is -

The integers m and p are such that 2 < m < p and m is not a factor of p. If r is the remainder when p is divided by m, is r >1?

1) the greatest common factor of m and p is 2. 2) the least common multiple of m and p is 30.

One of the explanations says

Quote:

when a number X is divided by number Y then the remainder left is always a multiple of HCF of X and Y ( provided x and y are integers) hence A is sufficient

Can someone please explain this? Why is this always true?

Guys please ignore if i ask a real dumb question.........but

Whenever we divide a bigger number with a smaller don't you agree that the remainder will be always > 1???

* When you divide 4 by 3, the remainder is 1. * When you divide 6 by 3, the remainder is 0.

When you divide an integer x by a positive integer d, all you can be sure of, without more information, is that the remainder is an integer between 0 and d-1, inclusive.
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