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Factors of zero
By Nigel Shelton on Thursday, November 23, 2000 - 04:44 pm:

Hello there,
I am a maths teacher for middle school aged pupils (10/11 year olds) and we have recently been exploring factors.
After defining a factor, one bright pupil asked if it was correct that zero had an infinite number of factors. His logic was that there were an infinite number of multiplications that resulted in an answer of zero;
0×0=0
1×0=0
2×0=0
3×0=0
...and so on...
I have never read a definition of factors that excluded the number zero. I have had interesting talks with other staff in the maths department but to no avail.
Is it correct that zero has an infinite number of factors or is the definition of a factor more precise than those offered by school maths text books?
Thank you very much in anticipation.
Best wishes,
Nigel Shelton

By James Lingard (Jchl2) on Friday, November 24, 2000 - 11:35 am:

I'd be inclined to agree with that - I can't think of any reason why these shouldn't be regarded as factors.

James.

By Anonymous on Friday, November 24, 2000 - 11:41 am:

A good definition of a factor/divisor is that an integer b is a factor of an integer a if and only if there exists an integer c such that a = cb.

This implies that any integer is a factor of 0 as you say. This is useful since then the highest common factor of 0 and n is equal to n, which is required for example in Euclid's algorithm. This would not be the case if n were not regarded as a factor of 0.