Q: What is the total or count of factors of the number 124,421,220?

 A: 288

How do I find the total factors of the number 124,421,220?

Step 1

Find the prime factorization of the number 124,421,220.

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

Factor Tree
124,421,220
Factor Arrows
262,210,610
Factor Arrows
231,105,305
Factor Arrows
310,368,435
Factor Arrows
33,456,145
Factor Arrows
5691,229
Factor Arrows
798,747
Factor Arrows
118,977
Factor Arrows
47191

The prime factorization in exponential form is: 22 x 32 x 51 x 71 x 111 x 471 x 1911

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)(g + 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.

124,421,220 = 22 x 32 x 51 x 71 x 111 x 471 x 1911
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)(g + 1)
Down Arrow
d(124421220) = (2 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(124421220) = (3)(3)(2)(2)(2)(2)(2)
Down Arrow
d(124421220) = 288

More numbers for you to try

Take a look at the factors page to see the factors of 124,421,220 and how to find them.

Try the factor calculator.

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