Question

Find the largest number which divides 320 and 457, leaving remainders 5 and 7 respectively.

Answer 1

We know that the required number divides 315 (320 – 5) and 450 (457 – 7).

∴ Required number = HCF (315, 450)

On applying Euclid’s lemma, we get: 

`315)450(1`
     – 315 
        135)315(2
            – 270 
                 45)135(3
                   – 135 
                        0

Therefore, the HCF of 315 and 450 is 45.

Hence, the required number is 45.