Question

What is the greatest number which divides 134 and 167 leaving 2 as the remainder in each case?

• A. 34
• B. 37
• C. 39
• D. 33

Answer 1

The correct option is D 33

The required number:
H.C.F of (134 - 2) and (167 - 2)
= H.C.F of 132 and 165

$\begin{array}{cc}2& 132\\ 2& 66\\ 3& 33\\ 11& 11\\ & 1\end{array}$
$\therefore 132=2\times 2\times 3\times 11$

$\begin{array}{cc}3& 165\\ 5& 55\\ 11& 11\\ & 1\end{array}$
$\therefore 165=3\times 5\times 11$
The common factors are 3, 11
Hence HCF of 132 and 165 = 3 $\times$ 11 = 33