What is the largest number that divides 626,3 | vedclass

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(B) To find the largest number that divides $626$,$3127$,and $15628$ leaving remainders $1$,$2$,and $3$ respectively,we subtract the remainders from t

Vedclass · Accepted Answer

$625$

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(B) To find the largest number that divides $626$,$3127$,and $15628$ leaving remainders $1$,$2$,and $3$ respectively,we subtract the remainders from the respective numbers:$626 - 1 = 625$$3127 - 2 = 3125$$15628 - 3 = 15625$Now,we need to find the Highest Common Factor $(HCF)$ of $625$,$3125$,and $15625$.Prime factorization of $625 = 5^4$Prime factorization of $3125 = 5^5$Prime factorization of $15625 = 5^6$The $HCF$ is the product of the lowest power of common prime factors,which is $5^4 = 625$.Therefore,the largest number is $625$.

What is the largest number that divides $626$,$3127$,and $15628$ and leaves remainders $1$,$2$,and $3$ respectively?

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