What least number must be subtracted from 13601 so that the remainder is divisible by 87?

Given data

• We want the smallest k ≥ 0 such that 13601 − k is divisible by 87.

Concept / Approach

• If N mod m = r, then subtracting r makes N − r divisible by m.

Step-by-step calculation

Compute 13601 ÷ 87.87 × 156 = 13572Remainder r = 13601 − 13572 = 29Therefore, least k = r = 29

Verification

13601 − 29 = 13572 = 87 × 156 (exact).

Common pitfalls

• Adding the remainder instead of subtracting it.

Final Answer

29