Find the greatest number that will divide 964 | vedclass

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Question

(A) To find the greatest number that divides $964, 1238,$ and $1400$ leaving remainders $41, 31,$ and $51$ respectively,we first subtract the remainde

Vedclass · Accepted Answer

$71$

Vedclass · Answer

(A) To find the greatest number that divides $964, 1238,$ and $1400$ leaving remainders $41, 31,$ and $51$ respectively,we first subtract the remainders from the respective numbers:$964 - 41 = 923$$1238 - 31 = 1207$$1400 - 51 = 1349$Now,we need to find the Highest Common Factor $(H.C.F.)$ of $923, 1207,$ and $1349$.First,find the $H.C.F.$ of $923$ and $1207$:$1207 = 923 	imes 1 + 284$$923 = 284 	imes 3 + 71$$284 = 71 	imes 4 + 0$So,the $H.C.F.$ of $923$ and $1207$ is $71$.Next,find the $H.C.F.$ of $71$ and $1349$:$1349 = 71 	imes 19 + 0$Since $1349$ is divisible by $71$,the $H.C.F.$ of $923, 1207,$ and $1349$ is $71$.Therefore,the greatest number is $71$.

Find the greatest number that will divide $964, 1238$ and $1400$ leaving remainders $41, 31$ and $51$ respectively.

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