A number leaves remainder 29 when divided by 56. What is the remainder when it is divided by 8?

Given data

• N ≡ 29 (mod 56)

Concept / Approach

• If m is a multiple of n, then N ≡ r (mod m) ⇒ N ≡ r (mod n). Here, 56 is a multiple of 8.

Step-by-step calculation

N = 56k + 29 ⇒ N mod 8 = (56k mod 8) + (29 mod 8)56k mod 8 = 0; 29 mod 8 = 5Therefore remainder = 5.

Common pitfalls

• Forgetting to reduce 29 modulo 8.

Final Answer

5