The greatest two digit number that will divided 398, 436, and 542 leaving respectively 7, 11 and 15 as remainders is

Correct Answer: 17

Solution

Subtracting the remainders gives $$398-7=391$$, $$436-11=425$$ and $$542-15=527$$, which must each be exactly divisible by the required number. Since $$391=17\times23$$, $$425=17\times25$$ and $$527=17\times31$$, their HCF is 17.

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