Q: What is the total or count of factors of the number 76,340,448?

 A: 96

How do I find the total factors of the number 76,340,448?

Step 1

Find the prime factorization of the number 76,340,448.

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

Factor Tree
76,340,448
Factor Arrows
238,170,224
Factor Arrows
219,085,112
Factor Arrows
29,542,556
Factor Arrows
24,771,278
Factor Arrows
22,385,639
Factor Arrows
3795,213
Factor Arrows
3265,071
Factor Arrows
388,357
Factor Arrows
149593

The prime factorization in exponential form is: 25 x 33 x 1491 x 5931

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.

76,340,448 = 25 x 33 x 1491 x 5931
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(76340448) = (5 + 1)(3 + 1)(1 + 1)(1 + 1)
Down Arrow
d(76340448) = (6)(4)(2)(2)
Down Arrow
d(76340448) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 76,340,448 and how to find them.

Try the factor calculator.

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