Q: What is the total or count of factors of the number 416,574,072?

 A: 48

How do I find the total factors of the number 416,574,072?

Step 1

Find the prime factorization of the number 416,574,072.

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

Factor Tree
416,574,072
Factor Arrows
2208,287,036
Factor Arrows
2104,143,518
Factor Arrows
252,071,759
Factor Arrows
317,357,253
Factor Arrows
35,785,751
Factor Arrows
7577,643

The prime factorization in exponential form is: 23 x 32 x 7571 x 7,6431

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.

416,574,072 = 23 x 32 x 7571 x 7,6431
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(416574072) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(416574072) = (4)(3)(2)(2)
Down Arrow
d(416574072) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 416,574,072 and how to find them.

Try the factor calculator.

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