Problem 2 · 2022 Math Kangaroo
Medium
Number Theory
divisionoff-by-one
How many positive three-digit numbers are divisible by 13?
Show answer
Answer: B — 69
Show hints
Hint 1 of 2
Count multiples of 13 up to 999, then remove those below 100.
Still stuck? Show hint 2 →
Hint 2 of 2
Use floor division: how many multiples of 13 are at most 999, and how many at most 99?
Show solution
Approach: count multiples by floor division
- Multiples of 13 up to 999: 999 / 13 = 76 (whole part).
- Multiples of 13 up to 99: 99 / 13 = 7.
- Three-digit ones: 76 − 7 = 69.
Mark:
· log in to save