Q: What is the total or count of factors of the number 13,635,216?

 A: 140

How do I find the total factors of the number 13,635,216?

Step 1

Find the prime factorization of the number 13,635,216.

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

Factor Tree
13,635,216
Factor Arrows
26,817,608
Factor Arrows
23,408,804
Factor Arrows
21,704,402
Factor Arrows
2852,201
Factor Arrows
3284,067
Factor Arrows
394,689
Factor Arrows
331,563
Factor Arrows
310,521
Factor Arrows
33,507
Factor Arrows
31,169
Factor Arrows
7167

The prime factorization in exponential form is: 24 x 36 x 71 x 1671

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)

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.

13,635,216 = 24 x 36 x 71 x 1671
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(13635216) = (4 + 1)(6 + 1)(1 + 1)(1 + 1)
Down Arrow
d(13635216) = (5)(7)(2)(2)
Down Arrow
d(13635216) = 140

More numbers for you to try

Take a look at the factors page to see the factors of 13,635,216 and how to find them.

Try the factor calculator.

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