Q: What is the total or count of factors of the number 5,424,160?

 A: 96

How do I find the total factors of the number 5,424,160?

Step 1

Find the prime factorization of the number 5,424,160.

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

Factor Tree
5,424,160
Factor Arrows
22,712,080
Factor Arrows
21,356,040
Factor Arrows
2678,020
Factor Arrows
2339,010
Factor Arrows
2169,505
Factor Arrows
533,901
Factor Arrows
74,843
Factor Arrows
29167

The prime factorization in exponential form is: 25 x 51 x 71 x 291 x 1671

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.

5,424,160 = 25 x 51 x 71 x 291 x 1671
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(5424160) = (5 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(5424160) = (6)(2)(2)(2)(2)
Down Arrow
d(5424160) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 5,424,160 and how to find them.

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