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Find the number of positive divisors of 540.

 Aug 6, 2020
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We first need to find the prime factorization of 540. This is 2 × 2 × 3 × 5 × 3 × 3, which is 2^2(3^3)(5^1).

Now, to find the amount of factors a number has, we need to multiply the exponent of each prime factor PLUS 1 by each other: https://www.math.upenn.edu/~deturck/m170/wk2/numdivisors.html (you can learn more here)

 

So, the number of prime factors is 3 x 4 x 2=24.

Therefore, 540 has 24 factors.

 Aug 6, 2020

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