A number leaves a remainder of 39 when divided by 357. What is the remainder when the same number is divided by 17?

Given data

• N ≡ 39 (mod 357)
• Find N mod 17

Concept / Approach

• Use modular arithmetic. If 357 is a multiple of 17, then N ≡ 39 (mod 17).

Step-by-step calculation357 = 17 × 21 ⇒ 357 ≡ 0 (mod 17)Therefore, N ≡ 39 (mod 17)39 ÷ 17 = 2 remainder 5 ⇒ 39 ≡ 5 (mod 17)

Quick checkAdd or subtract multiples of 17 from 39: 39 − 34 = 5.

Final Answer5