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

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answer is C.

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Detailed Solution

When number 398 divided by a number it gives 7 as remainder.
When number 436 divided by a number it gives 11 as remainder.
When number 542 divided by a number it gives 15 as remainder.
So, subtracting the remainders,

398 - 7 = 391

436 - 11 = 425

542 - 15 = 527

The highest common factor (H.C.F.) for these new integers is the number that divides 398, 436, and 542 while leaving the respective remainders.

391 = 17 \times 23

425 = 17 \times 5^{2}

527 = 17 \times 31

Here, H.C.F (391, 425, 527) = 17
So, 17 is the required number.
Correct option is 3.

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