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

∵ we are getting 5 and 7 as remainder.

Subtracting 5 and 7 from the dividends will give us the exact division.

So, let’s subtract the remainder and find the HCF of numbers (largest number which divides both the number) -

We need to find HCF of 320 - 5 = 315 and 457 - 7 = 450.

Prime factorization of numbers -

315 = 3 × 3 × 5 × 7

450 = 2 × 3 × 3 × 5 × 5

HCF of given numbers = 3 × 3 × 5 = 45.