Is ZERO a multiple of any number?

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- Sep 8th 2011, 01:56 PMonemachineIs ZERO a multiple of any number?
Is ZERO a multiple of any number?

- Sep 8th 2011, 02:05 PMskeeterRe: Is ZERO a multiple of any number?
see Dr. Math's answer ...

Math Forum - Ask Dr. Math - Sep 8th 2011, 02:17 PMTheBossRe: Is ZERO a multiple of any number?
I don't believe so.

- Sep 8th 2011, 02:22 PMPlatoRe: Is ZERO a multiple of any number?
- Sep 9th 2011, 03:39 AMHallsofIvyRe: Is ZERO a multiple of any number?
The usual definition of "x is a multiple of y" is "there exist an

**integer**, n, such that x= ny". Since 0 is an integer, and 0 times any number is 0, 0 is a multiple of**any**number.

Some special circumstance add the requirement that n be a**positive**integer- in which case the answer would be "no". However, those "special circumstances" typically are that we are only working with positive integers so the question would not arise so I will still say "yes, 0 is a multiple of any number." - Sep 9th 2011, 03:40 AMHallsofIvyRe: Is ZERO a multiple of any number?
- Sep 9th 2011, 04:54 AMCaptainBlackRe: Is ZERO a multiple of any number?