If a number is divisible by 624, the remainder will be 53, If the same number is divisible by 16, then the remainder will be:

When a number N leaves remainder 53 when divided by 624, we can write N = 624k + 53. To find the remainder when N is divided by 16, we need to compute (624k + 53) mod 16. Since 624 = 16 × 39, 624 is perfectly divisible by 16, so 624k mod 16 = 0. Therefore, N mod 16 = 53 mod 16 = 53 - 16×3 = 5. The key insight is that 624 is a multiple of 16, so only the remainder 53 matters.