Question

Find the greatest number which when divides $253,568$ and $813$ leaves the same remainder each time.

Answer 1

The greatest number which when divides $253,568$ and $813$ leaves the same remainder each time
$\to$ HCF of $(568-253),(813-568),(813-253)=$ HCF of $315,245$ and $560$

Prime factorisation of $315,245$ and $560$ is,

$315=3\times 3\times 5\times 7$
$245=7\times 7\times 5$
$560=2\times 2\times 2\times 2\times 5\times 7$

Therefore HCF of $315,245$ and $560$ is $5\times 7=35$.

The greatest number which when divides $253,568$ and $813$ leaves the same remainder each time is $35$ and the remainder obtained in each case is $8$.