Q: What is the total or count of factors of the number 301,415,044?

 A: 24

How do I find the total factors of the number 301,415,044?

Step 1

Find the prime factorization of the number 301,415,044.

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

Factor Tree
301,415,044
Factor Arrows
2150,707,522
Factor Arrows
275,353,761
Factor Arrows
710,764,823
Factor Arrows
67160,669

The prime factorization in exponential form is: 22 x 71 x 671 x 160,6691

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.

301,415,044 = 22 x 71 x 671 x 160,6691
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(301415044) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(301415044) = (3)(2)(2)(2)
Down Arrow
d(301415044) = 24

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Take a look at the factors page to see the factors of 301,415,044 and how to find them.

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