Problem 6 · 2022 Math Kangaroo
Medium
Number Theory
factorizationdigit-sum
The product of the digits of a ten-digit number is 15. How big is the sum of the digits of this number?
Show answer
Answer: D — 16
Show hints
Hint 1 of 2
Factor 15 into single digits.
Still stuck? Show hint 2 →
Hint 2 of 2
Fill the remaining digit places with 1s so the product stays 15, then add.
Show solution
Approach: force the nonzero digits
- 15 = 3 × 5; no single digit can be a 0 (that would zero the product).
- So the ten digits are 3, 5 and eight 1s.
- Digit sum = 3 + 5 + 8 = 16.
Mark:
· log in to save