Find the greatest positive integer that divid | vedclass

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Question

(A) To find the greatest positive integer that divides $70$ and $125$ leaving remainders $5$ and $8$ respectively,we need to find the Highest Common F

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(A) To find the greatest positive integer that divides $70$ and $125$ leaving remainders $5$ and $8$ respectively,we need to find the Highest Common Factor $(HCF)$ of $(70 - 5)$ and $(125 - 8)$.Step $1$: Subtract the remainders from the given numbers.$70 - 5 = 65$$125 - 8 = 117$Step $2$: Find the $HCF$ of $65$ and $117$.Prime factorization of $65 = 5 	imes 13$.Prime factorization of $117 = 3^2 	imes 13$.Step $3$: The common factor with the lowest power is $13$.Therefore,the greatest positive integer is $13$.

Find the greatest positive integer that divides $70$ and $125$ leaving remainders $5$ and $8$ respectively.

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