A number leaves a remainder of 29 when it is divided by 56. What is the remainder when the same number is divided by 8?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5
Let the number be \(N = 56k + 29\). Since \(56 = 8 \times 7\), the part \(56k\) is a multiple of 8 and leaves no remainder.
\(N \equiv 29 \pmod{8}\)
\(29 = 8 \times 3 + 5\)
So the remainder is 5. For example, \(N = 85\) gives \(85 = 8 \times 10 + 5\).