Q: What is the total or count of factors of the number 35,507,136?

 A: 112

How do I find the total factors of the number 35,507,136?

Step 1

Find the prime factorization of the number 35,507,136.

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

Factor Tree
35,507,136
Factor Arrows
217,753,568
Factor Arrows
28,876,784
Factor Arrows
24,438,392
Factor Arrows
22,219,196
Factor Arrows
21,109,598
Factor Arrows
2554,799
Factor Arrows
3184,933
Factor Arrows
726,419
Factor Arrows
29911

The prime factorization in exponential form is: 26 x 31 x 71 x 291 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)(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.

35,507,136 = 26 x 31 x 71 x 291 x 9111
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(35507136) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(35507136) = (7)(2)(2)(2)(2)
Down Arrow
d(35507136) = 112

More numbers for you to try

Take a look at the factors page to see the factors of 35,507,136 and how to find them.

Try the factor calculator.

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