Q: What is the total or count of factors of the number 358,878,720?

 A: 160

How do I find the total factors of the number 358,878,720?

Step 1

Find the prime factorization of the number 358,878,720.

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

Factor Tree
358,878,720
Factor Arrows
2179,439,360
Factor Arrows
289,719,680
Factor Arrows
244,859,840
Factor Arrows
222,429,920
Factor Arrows
211,214,960
Factor Arrows
25,607,480
Factor Arrows
22,803,740
Factor Arrows
21,401,870
Factor Arrows
2700,935
Factor Arrows
3233,645
Factor Arrows
546,729
Factor Arrows
83563

The prime factorization in exponential form is: 29 x 31 x 51 x 831 x 5631

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.

358,878,720 = 29 x 31 x 51 x 831 x 5631
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(358878720) = (9 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(358878720) = (10)(2)(2)(2)(2)
Down Arrow
d(358878720) = 160

More numbers for you to try

Take a look at the factors page to see the factors of 358,878,720 and how to find them.

Try the factor calculator.

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