A number leaves remainder 75 when divided by 296. What is the remainder when the same number is divided by 37?

Given data

• N ≡ 75 (mod 296).
• Note: 296 = 8 × 37.

Concept / Approach

• Reduce the remainder under the smaller modulus: N mod 37 = 75 mod 37 since 296 is a multiple of 37.

Step-by-step calculation

75 ÷ 37 = 2 remainder 1.Therefore, N ≡ 1 (mod 37).

Final Answer

Remainder = 1.