Q: What is the total or count of factors of the number 164,231,100?

 A: 216

How do I find the total factors of the number 164,231,100?

Step 1

Find the prime factorization of the number 164,231,100.

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

Factor Tree
164,231,100
Factor Arrows
282,115,550
Factor Arrows
241,057,775
Factor Arrows
313,685,925
Factor Arrows
34,561,975
Factor Arrows
5912,395
Factor Arrows
5182,479
Factor Arrows
1116,589
Factor Arrows
53313

The prime factorization in exponential form is: 22 x 32 x 52 x 111 x 531 x 3131

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)(f + 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.

164,231,100 = 22 x 32 x 52 x 111 x 531 x 3131
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(164231100) = (2 + 1)(2 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(164231100) = (3)(3)(3)(2)(2)(2)
Down Arrow
d(164231100) = 216

More numbers for you to try

Take a look at the factors page to see the factors of 164,231,100 and how to find them.

Try the factor calculator.

Explore more about the number 164,231,100:


Ask a Question