Q: What is the total or count of factors of the number 168,105,008?

 A: 40

How do I find the total factors of the number 168,105,008?

Step 1

Find the prime factorization of the number 168,105,008.

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

Factor Tree
168,105,008
Factor Arrows
284,052,504
Factor Arrows
242,026,252
Factor Arrows
221,013,126
Factor Arrows
210,506,563
Factor Arrows
19552,977
Factor Arrows
607911

The prime factorization in exponential form is: 24 x 191 x 6071 x 9111

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.

168,105,008 = 24 x 191 x 6071 x 9111
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(168105008) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(168105008) = (5)(2)(2)(2)
Down Arrow
d(168105008) = 40

More numbers for you to try

Take a look at the factors page to see the factors of 168,105,008 and how to find them.

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