Find the greatest number that will divide 43, | vedclass

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Question

(A) To find the greatest number that divides $43, 91,$ and $183$ leaving the same remainder,we calculate the differences between the numbers:$91 - 43

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) To find the greatest number that divides $43, 91,$ and $183$ leaving the same remainder,we calculate the differences between the numbers:$91 - 43 = 48$$183 - 91 = 92$$183 - 43 = 140$Now,we find the $HCF$ of these differences: $48, 92,$ and $140$.Prime factorization of $48 = 2^4 	imes 3$Prime factorization of $92 = 2^2 	imes 23$Prime factorization of $140 = 2^2 	imes 5 	imes 7$The common factor with the lowest power is $2^2 = 4$.Therefore,the greatest number is $4$.

Find the greatest number that will divide $43, 91$ and $183$ so as to leave the same remainder in each case.

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