Question

The greatest number that will divide $137,182and422$ leaving a reminder of $2$ in each case is

• A. $15$
• B. $12$
• C. $21$
• D. $22$

Answer 1

The correct option is A $15$

Given Numbers $137,182and422$

On dividing these given numbers by the greatest number we get reminder 2

From the given number subtracting 2

will get $135,180and420$

Now taking H.C.F of $135,180and420$

$135=3\times 3\times 3\times 5$

$180=2\times 2\times 3\times 3\times 5$

$420=2\times 2\times 3times5\times 7$

So the H.C. F of $135,180and420=3\times 5=15$

$\therefore thegreatestnumberrequired=15$