What is the least number that must be added to 5113 so that the sum is exactly divisible by 17?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4
Divide 5113 by 17 and find the remainder. The number to add is 17 minus the remainder, which takes the sum up to the next multiple of 17.
\(5113=17\times300+13\)
Number to add \(=17-13=4\)
Check: \(5113+4=5117=17\times301\)
The least number to be added is 4.
Why the other options are incorrect
Option (2) 3 — Incorrect. \(5113+3=5116\), which leaves remainder 16 when divided by 17.
Option (3) 6 — Incorrect. \(5113+6=5119\), which leaves remainder 2 when divided by 17.
Option (4) 13 — Incorrect. 13 is the remainder of 5113 ÷ 17; it is the number to be subtracted, not added (5113 + 13 = 5126 is not a multiple of 17).