Question

If $1125=3^m\times 5^n;$ find m and n.

Answer 1

$1125=3^2\times 5^3$

The factors of 1125 are $3\times 3\times 5\times 5\times 5$

$\begin{array}{cc}3& 1125\\ 3& 375\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$

$\therefore 1125=3\times 3\times 5\times 5\times 5\text{Now comparing},3^2\times 5^3=3^m\times 5^n\therefore m=2n=3$