Q: What is the total or count of factors of the number 4,378,800?

 A: 120

How do I find the total factors of the number 4,378,800?

Step 1

Find the prime factorization of the number 4,378,800.

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

Factor Tree
4,378,800
Factor Arrows
22,189,400
Factor Arrows
21,094,700
Factor Arrows
2547,350
Factor Arrows
2273,675
Factor Arrows
391,225
Factor Arrows
518,245
Factor Arrows
53,649
Factor Arrows
4189

The prime factorization in exponential form is: 24 x 31 x 52 x 411 x 891

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)

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.

4,378,800 = 24 x 31 x 52 x 411 x 891
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(4378800) = (4 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(4378800) = (5)(2)(3)(2)(2)
Down Arrow
d(4378800) = 120

More numbers for you to try

Take a look at the factors page to see the factors of 4,378,800 and how to find them.

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