Question

long answer type question

find the largest number which on dividing 1251 and 9377 and 15628 leaves remainder 1 2 and 3 respectively​

Answer 1

$\small \bold \red{Subtract \: 1, 2, 3 \: from \: 1251, 9377, 15628}$

$\small \bold \red{respectively.}$

$\bold \red{1251 - 1 = 1250, }$

$\bold \red{9377 - 2 = 9375, }$

$\bold \red{15628 - 3 = 15625}$

$\small\bold \red{Find \: the \: HCF \: of \: 1250 \: and \: 9375 }$

$\red{9375 = 1250 \times 7 + 625 }$

$\red{1250 = 625 \times 2 + 0 }$

$\bold \red{thus \: 625 \: is \: the \: HCF }$

$\small \bold \red{Now, find \: the \: HCF \: of \: 625 \: and \: 15625 }$

$\red{15625 = 625 \times 25 + 0 }$

So, 625 is the number that divides 1251, 9377 and 15628 leaving the remainders 1, 2 and 3 respective.