Find the number of distinct positive divisors of 21600 (inclusive of 1 and itself).
(1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600) >>Total = 72 such numbers.
+781 We find the prime factorization of 21600:
2^5 x 3^3 x 5^2.
The number of multiples must be (5+1)(3+1)(2+1)=6*4*3=72 divisors.
