The largest positive integer that divides 70 | vedclass

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Question

(A) To find the largest positive integer that divides $70$ and $125$ leaving remainders $5$ and $8$ respectively,we subtract the remainders from the n

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(A) To find the largest positive integer that divides $70$ and $125$ leaving remainders $5$ and $8$ respectively,we subtract the remainders from the numbers first.$70 - 5 = 65$$125 - 8 = 117$Now,we need to find the Greatest Common Divisor $(GCD)$ of $65$ and $117$.Prime factorization of $65 = 5 	imes 13$Prime factorization of $117 = 3^2 	imes 13$The common factor is $13$.Therefore,the largest positive integer is $13$.

The largest positive integer that divides $70$ and $125$,leaving remainders $5$ and $8$ respectively,is:

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