Q: What is the total or count of factors of the number 37,707,264?

 A: 180

How do I find the total factors of the number 37,707,264?

Step 1

Find the prime factorization of the number 37,707,264.

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

Factor Tree
37,707,264
Factor Arrows
218,853,632
Factor Arrows
29,426,816
Factor Arrows
24,713,408
Factor Arrows
22,356,704
Factor Arrows
21,178,352
Factor Arrows
2589,176
Factor Arrows
2294,588
Factor Arrows
2147,294
Factor Arrows
273,647
Factor Arrows
324,549
Factor Arrows
38,183
Factor Arrows
71,169
Factor Arrows
7167

The prime factorization in exponential form is: 29 x 32 x 72 x 1671

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.

37,707,264 = 29 x 32 x 72 x 1671
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(37707264) = (9 + 1)(2 + 1)(2 + 1)(1 + 1)
Down Arrow
d(37707264) = (10)(3)(3)(2)
Down Arrow
d(37707264) = 180

More numbers for you to try

Take a look at the factors page to see the factors of 37,707,264 and how to find them.

Try the factor calculator.

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