Q: What is the total or count of factors of the number 135,264?

 A: 24

How do I find the total factors of the number 135,264?

Step 1

Find the prime factorization of the number 135,264.

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

Factor Tree
135,264
Factor Arrows
267,632
Factor Arrows
233,816
Factor Arrows
216,908
Factor Arrows
28,454
Factor Arrows
24,227
Factor Arrows
31,409

The prime factorization in exponential form is: 25 x 31 x 1,4091

Step 2

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

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

135,264 = 25 x 31 x 1,4091
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(135264) = (5 + 1)(1 + 1)(1 + 1)
Down Arrow
d(135264) = (6)(2)(2)
Down Arrow
d(135264) = 24

More numbers for you to try

Take a look at the factors page to see the factors of 135,264 and how to find them.

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