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

Subtract the remainders first: 320 - 5 = 315 and 457 - 7 = 450. The required number is HCF(315, 450). $315=3^2\times 5\times 7$ and $450=2\times 3^2\times 5^2$, so HCF = $3^2\times$ 5 = 45. Answering 137 uses the difference 457 - 320 without removing the remainders; 15 is a common factor but not the greatest; 90 divides 450 but not 315.