Q: What is the total or count of factors of the number 30,871,470?

 A: 48

How do I find the total factors of the number 30,871,470?

Step 1

Find the prime factorization of the number 30,871,470.

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

Factor Tree
30,871,470
Factor Arrows
215,435,735
Factor Arrows
35,145,245
Factor Arrows
51,029,049
Factor Arrows
7147,007
Factor Arrows
721,001

The prime factorization in exponential form is: 21 x 31 x 51 x 72 x 21,0011

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.

30,871,470 = 21 x 31 x 51 x 72 x 21,0011
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(30871470) = (1 + 1)(1 + 1)(1 + 1)(2 + 1)(1 + 1)
Down Arrow
d(30871470) = (2)(2)(2)(3)(2)
Down Arrow
d(30871470) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 30,871,470 and how to find them.

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