Q: What is the total or count of factors of the number 301,815,144?

 A: 96

How do I find the total factors of the number 301,815,144?

Step 1

Find the prime factorization of the number 301,815,144.

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

Factor Tree
301,815,144
Factor Arrows
2150,907,572
Factor Arrows
275,453,786
Factor Arrows
237,726,893
Factor Arrows
312,575,631
Factor Arrows
34,191,877
Factor Arrows
17246,581
Factor Arrows
1911,291

The prime factorization in exponential form is: 23 x 32 x 171 x 1911 x 1,2911

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.

301,815,144 = 23 x 32 x 171 x 1911 x 1,2911
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(301815144) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(301815144) = (4)(3)(2)(2)(2)
Down Arrow
d(301815144) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 301,815,144 and how to find them.

Try the factor calculator.

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