Q: What is the total or count of factors of the number 468,276,736?

 A: 80

How do I find the total factors of the number 468,276,736?

Step 1

Find the prime factorization of the number 468,276,736.

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

Factor Tree
468,276,736
Factor Arrows
2234,138,368
Factor Arrows
2117,069,184
Factor Arrows
258,534,592
Factor Arrows
229,267,296
Factor Arrows
214,633,648
Factor Arrows
27,316,824
Factor Arrows
23,658,412
Factor Arrows
21,829,206
Factor Arrows
2914,603
Factor Arrows
1948,137
Factor Arrows
371,301

The prime factorization in exponential form is: 29 x 191 x 371 x 1,3011

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.

468,276,736 = 29 x 191 x 371 x 1,3011
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(468276736) = (9 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(468276736) = (10)(2)(2)(2)
Down Arrow
d(468276736) = 80

More numbers for you to try

Take a look at the factors page to see the factors of 468,276,736 and how to find them.

Try the factor calculator.

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