Find the greatest number that will divide 517 and 815 leaving the reminders 1 and 3 respectively

Given :

The given numbers are 517 and 815 which leaves the remainders 1 and 3 respectively when we divide by a number.

To do :

We have to find the number.

Solution :

Let the number be 'x'.

When we divide 517 and 815 by x the remainder is 1 and 3.

$517 - 1 = 516$

$815 - 3 = 812$

Now, when we divide 516 and 812 by x the remainder will be 0.

Therefore, x is the HCF of 516 and 812.

Factors of $516 =2 \times 2\times 3 \times 43 = 2^2 \times 3 \times 43$

Factors of 812 $= 2 \times 2 \times 7 \times 29 = 2^2 \times 7 \times 29$

$HCF = Common prime factors with lowest powers$

Therefore, HCF of 516 and 812 is $2^2 = 4$

Therefore, the greatest number will divide 517 and 815 leaving reminders 1 and 3 respectively is 4.