Question

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

Answer 1

Subtracting the remainders from given numbers

we have,

$626-1=625$

$3127-2=3125$

$15628-1=15625$

Now the factors of the above numbers are,

$625=5\times 5\times 5\times 5$

$3125=5\times 5\times 5\times 5\times 5$

$156125=5\times 5\times 5\times 5\times 5\times 5$

The HCF of following numbers $\Rightarrow 625$

Hence $625$ is the largest number that divides

626626, 31273127 and 1562815628 and leaves remainders of 1,21,2 and 33 respectively.