On dividing a number by 56 , we get 29 as remainder . On dividing the same…
2023
On dividing a number by 56 , we get 29 as remainder . On dividing the same number by 8, what will be the remainder ?
- A.
2
- B.
3
- C.
4
- D.
5
Attempted by 6 students.
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Correct answer: D
Answer: 5
Reason: Let the number be n. Since dividing n by 56 leaves remainder 29, we can write n = 56q + 29 for some integer q.
When dividing by 8, the term 56q is divisible by 8 (because 56 = 7×8), so it contributes no remainder. Therefore the remainder equals the remainder when 29 is divided by 8.
Compute 29 ÷ 8: 29 = 3×8 + 5, so the remainder is 5.
Hence, when the number is divided by 8 the remainder is 5.