Problem Statement
A number is divided by 357 and leaves remainder 5. What will be the remainder when the same number is divided by 17?
Explanation
Let the number be N. According to the problem, N equals 357q plus 5 where q is the quotient. We need to find the remainder when N is divided by 17.
First, observe that 357 equals 17 times 21. So N equals 17 times 21q plus 5 equals 17 times 21q plus 5. When we divide N by 17: N divided by 17 equals open parenthesis 17 times 21q plus 5 close parenthesis divided by 17 equals 21q plus 5 divided by 17. Since 17 times 21q is perfectly divisible by 17, the remainder depends only on 5 divided by 17. As 5 is less than 17, the remainder is 5 itself. This works because 357 is a multiple of 17, so the remainder remains unchanged.
Code Solution
SolutionRead Only
// Given: Number ÷ 357 leaves remainder 5 // Let Number = N = 357q + 5 // Find: N ÷ 17 = ? // Key observation: 357 = 17 × 21 // Therefore: // N = 357q + 5 // N = (17 × 21)q + 5 // N = 17(21q) + 5 // When divided by 17: // N/17 = [17(21q) + 5]/17 // = 21q + 5/17 // Since 5 < 17: // Remainder = 5 // Verification: // Let N = 362 (357×1 + 5) // 362 ÷ 17 = 21 remainder 5 ✓
Practice Sets
This question appears in the following practice sets:
