Question

Find the largest positive integer that will divide $398,436$ and $542$ leaving remainders $7,11$ and $15$ respectively.

• A. $15$
• B. $16$
• C. $17$
• D. $18$

Answer 1

The correct option is C $17$

Deducting the remainders from numbers we get,

$398-7=391$

$436-11=425$

$542-15=527$

H.C.F of these new numbers is the largest possible number that divides $398,436,542$ leaving respective remainders

$391=17\times 23$

$425=17\times 5^2$

$527=17\times 31$

$\therefore$ Answer $=$ H.C.F$(391,425,527)=17$