Q: What is the total or count of factors of the number 106,504,128?

 A: 42

How do I find the total factors of the number 106,504,128?

Step 1

Find the prime factorization of the number 106,504,128.

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

Factor Tree
106,504,128
Factor Arrows
253,252,064
Factor Arrows
226,626,032
Factor Arrows
213,313,016
Factor Arrows
26,656,508
Factor Arrows
23,328,254
Factor Arrows
21,664,127
Factor Arrows
3554,709
Factor Arrows
3184,903

The prime factorization in exponential form is: 26 x 32 x 184,9031

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.

106,504,128 = 26 x 32 x 184,9031
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(106504128) = (6 + 1)(2 + 1)(1 + 1)
Down Arrow
d(106504128) = (7)(3)(2)
Down Arrow
d(106504128) = 42

More numbers for you to try

Take a look at the factors page to see the factors of 106,504,128 and how to find them.

Try the factor calculator.

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