Q: What is the total or count of factors of the number 501,150,100?

 A: 72

How do I find the total factors of the number 501,150,100?

Step 1

Find the prime factorization of the number 501,150,100.

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

Factor Tree
501,150,100
Factor Arrows
2250,575,050
Factor Arrows
2125,287,525
Factor Arrows
525,057,505
Factor Arrows
55,011,501
Factor Arrows
11455,591
Factor Arrows
895,119

The prime factorization in exponential form is: 22 x 52 x 111 x 891 x 5,1191

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.

501,150,100 = 22 x 52 x 111 x 891 x 5,1191
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(501150100) = (2 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(501150100) = (3)(3)(2)(2)(2)
Down Arrow
d(501150100) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 501,150,100 and how to find them.

Try the factor calculator.

Explore more about the number 501,150,100:


Ask a Question