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Daily puzzle · 2026-10-24 · Divisibility

Mathbound Daily Puzzle — 2026-10-24 — Divisibility Solution

Level 2

How many positive integers k≤72k\le 72 satisfy gcd⁡(k,72)=1\gcd(k,72)=1?
  1. A.71
  2. B.36
  3. C.24
  4. D.16
  5. E.34

Answer: C

Key idea: Euler totient φ(n)\varphi(n).

Set it up: Factor 72.

Solution: 2424.

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Mathbound Daily Puzzle — 2026-10-24 — Divisibility Solution