Question

Find the GCD:

(11) 585, 675, 540

Answer 1

$\begin{array}{cc}3& 585\\ 3& 195\\ 5& 65\\ 13& 13\\ & 1\end{array}$
⇒ 585 = 3 × 3 × 5 × 13

$\begin{array}{cc}3& 675\\ 3& 225\\ 3& 75\\ 5& 25\\ 5& 5\\ & 1\end{array}$
⇒ 675 = 3 × 3 × 3 × 5 × 5

$\begin{array}{cc}2& 540\\ 2& 270\\ 3& 135\\ 3& 45\\ 3& 15\\ 5& 5\\ & 1\end{array}$
⇒ 540 = 2 × 2 × 3 × 3 × 3 × 5
∴ GCD = 3 × 3 × 5 = 45