Find the greatest number which will divide 25 | vedclass

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Question

(C) To find the greatest number that leaves the same remainder when dividing $25, 73,$ and $97$,we calculate the differences between the numbers:$73 -

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(C) To find the greatest number that leaves the same remainder when dividing $25, 73,$ and $97$,we calculate the differences between the numbers:$73 - 25 = 48$$97 - 73 = 24$$97 - 25 = 72$Now,find the $H.C.F.$ of these differences: $48, 24,$ and $72$.The prime factorization of the numbers is:$48 = 2^4 	imes 3$$24 = 2^3 	imes 3$$72 = 2^3 	imes 3^2$The $H.C.F.$ is the product of the lowest powers of common prime factors: $2^3 	imes 3 = 8 	imes 3 = 24$.Thus,the greatest number is $24$.

Find the greatest number which will divide $25, 73$ and $97$ so as to leave the same remainder in each case.

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