Question

Find the largest positive integer that will divide$398,436$ and $542$ leaving remainders$7,11$ and$15$ respectively.

Answer 1

Solve for the HCF of the given numbers by deducting the given remainders

Subtracting the remainders from numbers we get,

$\Rightarrow$ $398-7=391$ [As the remainder is $7$]

$\Rightarrow 436-11=425$ [As the remainder is $11$]

$\Rightarrow$$542-15=527$ [As the remainder is $15$]

HCF of these new numbers is the largest number that divides $398,436,542$ leaving respective remainders.

Factors of$391=17\times 23$

Factors of $425=17\times 52$

Factors of $527=17\times 31$

The HCF of $391,425,527$ is$17$.

Hence, the largest positive integer that will divide $398,436$ and$542$, leaving remainders$7,11$ and$15$ respectively is$17$.