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Find the number of distinct positive divisors of 21600 (inclusive of 1 and itself).

 Jul 6, 2020
 #1
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(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.

 Jul 6, 2020
 #2
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+1

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.

 Jul 6, 2020

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