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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

`15`

B

`16`

C

`17`

D

`18`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `N_1 , `N_2 , `N_3` be the exact numbers which when divided by largest number does not leave remainder
`N_1= 398-7= 391`
`N_2= 436-11 = 425`
`N_3 = 542-15 = 527`
Now,
`N_1= 391= 23*17`
`N_2= 425 = 17*5*5`
`N_3= 527= 31*17`
`HCF= 17`
...
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