Question

Express each of the following as product of powers of their prime factors:

$\left(i\right)$ $648$ $\left(ii\right)$ $405$

$\left(iii\right)$ $540$ $\left(iv\right)$ $3,600$

Answer 1

(i) $648=2\times 2\times 2\times 3\times 3\times 3\times 3=2^3\times 3^4$

$\begin{array}{cc}2& 648\\ 2& 324\\ 2& 162\\ 3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

(ii) $405=3\times 3\times 3\times 3\times 5=3^4\times 5$

$\begin{array}{cc}3& 405\\ 3& 135\\ 3& 45\\ 3& 15\\ 5& 5\\ & 1\end{array}$

(iii) $540=2\times 2\times 3\times 3\times 3\times 5=2^2\times 3^3\times 5$

$\begin{array}{cc}2& 540\\ 2& 270\\ 3& 135\\ 3& 45\\ 3& 15\\ 5& 5\\ & 1\end{array}$

(iv) $3600=2\times 2\times 2\times 2\times 3\times 3\times 5\times 5=2^4\times 3^2\times 5^2$

$\begin{array}{cc}2& 3600\\ 2& 1800\\ 2& 900\\ 2& 450\\ 3& 225\\ 3& 75\\ 5& 25\\ 5& 5\\ & 1\end{array}$
​​​​​​​​​​​​​​​​