Q: What is the total or count of factors of the number 36,405,684?

 A: 72

How do I find the total factors of the number 36,405,684?

Step 1

Find the prime factorization of the number 36,405,684.

Use a factor tree to assist with solving. Take a look at our prime factorization page for additional help.

Factor Tree
36,405,684
Factor Arrows
218,202,842
Factor Arrows
29,101,421
Factor Arrows
33,033,807
Factor Arrows
31,011,269
Factor Arrows
7144,467
Factor Arrows
731,979

The prime factorization in exponential form is: 22 x 32 x 71 x 731 x 1,9791

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)

Where d(n) is equal to the number of divisors of the number and a, b, etc. are equal to the exponents of the prime factorization.

Now substitute the letters in the equation with the the exponents of your prime factorization and then solve to calculate the total number of divisors.

36,405,684 = 22 x 32 x 71 x 731 x 1,9791
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(36405684) = (2 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(36405684) = (3)(3)(2)(2)(2)
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d(36405684) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 36,405,684 and how to find them.

Try the factor calculator.

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