Explanation

With 72 = m×n and 1 < m < n, m must be a proper divisor of 72 smaller than √72 ≈ 8.49. The divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; those strictly between 1 and √72 are 2, 3, 4, 6 and 8 — five values (8 pairs with 9, still satisfying m < n). Hence there are 5 possible values of m.