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Find the largest number that will divide...

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

A

`17`

B

`18`

C

`19`

D

`20`

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly the required number divides ( 398 -7) = 391
( 436 -11) = 425 and ( 542 -15) = 527 exactly.
required number = HCF ( 391,425, 527)
Now, 391, = `( 17xx 23)`
` 425 = ( 5^(2) xx 17)`
` 527 = ( 17xx 31)`
HCF ( 391,425 ,527) - 17`
Hence, the required number is 17.
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