Q: What is the total or count of factors of the number 105,507,684?

 A: 144

How do I find the total factors of the number 105,507,684?

Step 1

Find the prime factorization of the number 105,507,684.

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

Factor Tree
105,507,684
Factor Arrows
252,753,842
Factor Arrows
226,376,921
Factor Arrows
38,792,307
Factor Arrows
32,930,769
Factor Arrows
3976,923
Factor Arrows
3325,641
Factor Arrows
3108,547
Factor Arrows
195,713
Factor Arrows
29197

The prime factorization in exponential form is: 22 x 35 x 191 x 291 x 1971

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.

105,507,684 = 22 x 35 x 191 x 291 x 1971
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(105507684) = (2 + 1)(5 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(105507684) = (3)(6)(2)(2)(2)
Down Arrow
d(105507684) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 105,507,684 and how to find them.

Try the factor calculator.

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