Q: What is the total or count of factors of the number 135,013,032?

 A: 240

How do I find the total factors of the number 135,013,032?

Step 1

Find the prime factorization of the number 135,013,032.

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

Factor Tree
135,013,032
Factor Arrows
267,506,516
Factor Arrows
233,753,258
Factor Arrows
216,876,629
Factor Arrows
35,625,543
Factor Arrows
31,875,181
Factor Arrows
7267,883
Factor Arrows
738,269
Factor Arrows
75,467
Factor Arrows
7781
Factor Arrows
1171

The prime factorization in exponential form is: 23 x 32 x 74 x 111 x 711

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.

135,013,032 = 23 x 32 x 74 x 111 x 711
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(135013032) = (3 + 1)(2 + 1)(4 + 1)(1 + 1)(1 + 1)
Down Arrow
d(135013032) = (4)(3)(5)(2)(2)
Down Arrow
d(135013032) = 240

More numbers for you to try

Take a look at the factors page to see the factors of 135,013,032 and how to find them.

Try the factor calculator.

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