Q: What is the total or count of factors of the number 37,309,888?

 A: 112

How do I find the total factors of the number 37,309,888?

Step 1

Find the prime factorization of the number 37,309,888.

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

Factor Tree
37,309,888
Factor Arrows
218,654,944
Factor Arrows
29,327,472
Factor Arrows
24,663,736
Factor Arrows
22,331,868
Factor Arrows
21,165,934
Factor Arrows
2582,967
Factor Arrows
783,281
Factor Arrows
117,571
Factor Arrows
67113

The prime factorization in exponential form is: 26 x 71 x 111 x 671 x 1131

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.

37,309,888 = 26 x 71 x 111 x 671 x 1131
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(37309888) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(37309888) = (7)(2)(2)(2)(2)
Down Arrow
d(37309888) = 112

More numbers for you to try

Take a look at the factors page to see the factors of 37,309,888 and how to find them.

Try the factor calculator.

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