Question

find the greatest divider when divided by 357, 192 & 252. least same remainder in each case

Answer 1

take difference of these three numbers with one another and then HCF

357-192
252-192
357-252

now find HCF

Answer 2

Greatest divider when divided by 357, 192 & 252. least same remainder in each case is 1.

Given:

357, 192 and 252

To find:

Greatest divider when divided by 357, 192 & 252. least same remainder in each case

Solution:

There is a concept that that if we have 3 numbers b, c and d then the greatest number that will divide all three of them leaving the same remainder will be the H.C.F of (b-a), (c-b), (c-a).

So,

a = 192

b = 252

c = 357

(b-a) = 252 - 192 = 60

(c-b) =  357- 252 = 121

(c-a) = 357 - 192 = 165

Now we have to find H.C.F. of 60, 121, 165

Using factorisation method,

60 = 1*2*2*3*5

121 = 1*11*11

165 = 1*3*5*11

So, the common factor is only 1

H.C.F = 1

Hence, greatest divider when divided by 357, 192 & 252. least same remainder in each case is 1.

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