Q: What is the total or count of factors of the number 308,348,880?

 A: 160

How do I find the total factors of the number 308,348,880?

Step 1

Find the prime factorization of the number 308,348,880.

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

Factor Tree
308,348,880
Factor Arrows
2154,174,440
Factor Arrows
277,087,220
Factor Arrows
238,543,610
Factor Arrows
219,271,805
Factor Arrows
36,423,935
Factor Arrows
51,284,787
Factor Arrows
7183,541
Factor Arrows
296,329

The prime factorization in exponential form is: 24 x 31 x 51 x 71 x 291 x 6,3291

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)(f + 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.

308,348,880 = 24 x 31 x 51 x 71 x 291 x 6,3291
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(308348880) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(308348880) = (5)(2)(2)(2)(2)(2)
Down Arrow
d(308348880) = 160

More numbers for you to try

Take a look at the factors page to see the factors of 308,348,880 and how to find them.

Try the factor calculator.

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