Find the remainder when 17,200 is divided by 18.

Given data

• Dividend: 17,200
• Divisor: 18

Concept / Approach

• Use either direct division or modular reasoning with coprime factors: 18 = 2 × 9.
• We need an r such that 0 ≤ r < 18, r ≡ 0 (mod 2) and r ≡ 17,200 (mod 9).

Step-by-step calculation (direct)

18 × 955 = 17,190Remainder r = 17,200 − 17,190 = 10

Step-by-step (mod reasoning)

17,200 mod 9: digit sum = 1+7+2 = 10 ⇒ 10 mod 9 = 1 ⇒ r ≡ 1 (mod 9)Also r must be even (since 17,200 is even).Even residues < 18 that are ≡ 1 (mod 9): {10}. Hence r = 10.

Common pitfalls

• Confusing remainder with quotient.
• Forgetting the remainder must be less than the divisor.

Final Answer

Remainder = 10.