We have to find a number , which divides the other number means `to` H.C.F.
It is given that the required number , when divides 400 , 437 and 542 leaving remainders 9 , 12 and 15 respectively . It means that if 400 is 9 less , 437 is 12 less and 542 is 15 less , then on division , gives no remainder (extra) .
`therefore 400 - 9 = 391 , 437 - 12 = 425` and 542 - 15 = 527 are completely divisible by the required number .
First we will find the H.C.F. of 391 and 425 .
`therefore " " 425 = 391 xx 1 + 34`
`391 = 34 xx 11 + 17`
`34 = 17 xx 2 + 0`
`therefore` H.C.F. (391, 425) = 17
Now , we will find the H.C.F. of 17 and 527.
`therefore " " 527 = 17 xx 31 + 0`
`implies " "` H.C.F. (17, 527) = 17
`therefore` Required number = 17
