How many of the positive divisors of 2160 are multiples of 3?

1 answer:

5 0

30 of the divisors are multiples of 3

The factors of 2160 are 1, 2160, 2, 1080, 3, 720, 4, 540, 5, 432, 6, 360, 8, 270, 9, 240, 10, 216, 12, 180, 15, 154, 16, 135, 18, 120, 20, 108, 24, 90, 27, 80, 30, 72, 36, 60, 40, 54, 45, 48
These are all divisors of 2160 but only 30 are multiples of 3.
The ones that are NOT are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80

You can also do this using prime factors 2x2x2x2x3x3x3x5 = 2160 but it is harder to explain.

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