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# Find the largest number that will divide 397, 435, 541 leaving remainder 6, 10, 14, respectively. Solve it.

** Given:** a largest number will divide 397,435, and 541 and leave remainder 6,10, and14 respectively.

** To find:** We have to find that largest number.

__Solution: __

If that number divide 397, 435, 541 leaving remainder 6, 10, 14 respectively, this means that number will divide 391(397 - 6), 425(435 - 10) and 527(541 - 14) completely.

Now, we just have to find the HCF of 391, 425 and 527.

HCF of 391, 425 and 527:

Factors of 391 = 17 x 23

Factors of 425 = 5 x 5 x 17

Factors of 527 = 17 x 31

Now the highest common factor is 17.

So the largest number that will divide 397, 435, 541 leaving remainder 6, 10, 14

respectively is 17.

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