Question

What is the greatest number that divides $720$ and $810$ without leaving any remainder?

Answer 1

Suppose we have two numbers A and B and the greatest number which divides both A and B is the greatest common factor of A and B.

Now we have to find $g.c.d$ of $720$ and $810$.

Since for any number we can factories in its prime factors then,

$720=2\times 2\times 2\times 2\times 3\times 3\times 5$;

$810=2\times 3\times 3\times 3\times 3\times 5$

Then greatest common factor is $2\times 3\times 3\times 5=90$, then $90$ is the greatest number that divides $720$ and $810$.