Question

What is the largest number that can divide $410,751,1030$ leaving $7$ as a remainder in each case?

Answer 1

b'

$410–7=403$

$751–7=744$

$1030–7=1023$

Required number$=$HCF of $403,744$ and $1023$.

We know that $403=13\times 31$,

$744=2\times 2\times 2\times 3\times 31$ and

$1023=3\times 11\times 31$

HCF$=31$

$\therefore$ Required number$=31$

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