Q: What is the total or count of factors of the number 234,303,264?

 A: 72

How do I find the total factors of the number 234,303,264?

Step 1

Find the prime factorization of the number 234,303,264.

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

Factor Tree
234,303,264
Factor Arrows
2117,151,632
Factor Arrows
258,575,816
Factor Arrows
229,287,908
Factor Arrows
214,643,954
Factor Arrows
27,321,977
Factor Arrows
32,440,659
Factor Arrows
3813,553
Factor Arrows
1362,581

The prime factorization in exponential form is: 25 x 32 x 131 x 62,5811

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.

234,303,264 = 25 x 32 x 131 x 62,5811
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(234303264) = (5 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(234303264) = (6)(3)(2)(2)
Down Arrow
d(234303264) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 234,303,264 and how to find them.

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