Calculus/Proof

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Question
Prove: For integers a, b, and c, if a is a factor of b, and b is a factor of c, then a is a factor of c.

Answer
Hi Sandra,
The simple way to consider it is this;
If A is a factor of B, then we can write
B = Am
where m is an integer
In the same way, if B is a factor of C, then we can write
C = Bn
where n is an integer

We therefore have,
C = (Am)n
= A(mn)
and so A is a factor of C, since mn is the product of two integers and hence an integer itself.

Regards

Calculus

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