Question

Express each number as a product of its prime factors:
(i) $140$ (ii) $156$ (iii) $3825$

Answer 1

We have

(i) $\begin{array}{cc}2& 140\\ 2& 70\\ 5& 35\\ 7& 7\\ & 1\end{array}$

$\therefore 140=7\times 5\times 2^2$

(ii) $\begin{array}{cc}2& 156\\ 2& 78\\ 3& 39\\ 13& 13\\ & 1\end{array}$

$\therefore 156=13\times 3\times 2^2$

(iii) $\begin{array}{cc}3& 3825\\ 3& 1275\\ 5& 425\\ 5& 85\\ 17& 17\\ & 1\end{array}$

$\therefore 3825=17\times 3^2\times 5^2$.

These are the required prime factorization.