# Math Help - Prooving Factors

1. ## Prooving Factors

How would I prove that 4 is a factor of 6a x 10b ?

2. ## Re: Prooving Factors

Originally Posted by calmo11
How would I prove that 4 is a factor of 6a x 10b ?
is 4 a factor of 60?

3. ## Re: Prooving Factors

Yes, how does that relate to the above?

4. ## Re: Prooving Factors

Is it like you say 6a x 10b = 4t
60ab=4t
4(15ab)=4t
If 15ab is an integer
Then let 15ab=t
4t=4t ?

5. ## Re: Prooving Factors

Assuming $a, b \in \mathbb{Z}$

$\dfrac{6a \times 10b}{4}=\dfrac{60ab}{4}=15ab \in \mathbb{Z}$

The last statement by closure of multiplication over the integers.

and so $4 \times 15ab = 6a \times 10b$ and 4 is thus a factor of $6a \times 10b$

That's really all there is to it.