Question

The greatest number which divides $77,147$ and $252$ leaving the same remainder $7$ in each case is

• A. $9$
• B. $15$
• C. $25$
• D. $35$

Answer 1

The correct option is D $35$

Look at the common differences:

$\Rightarrow$ $147-77=70$

$\Rightarrow$ $252-147=105$

$\Rightarrow$ Now, we have to find H.C.F of $70$ and $105$

$\Rightarrow$ $70=2\times 5\times 7$

$\Rightarrow$ $105=3\times 5\times 7$

$\Rightarrow$ Common factor $=7\times 5=35$

$\therefore$ The greatest number which divides $77,147$ and $252$ leaving the same remainder in each case is $35$.