Q: What is the total or count of factors of the number 12,421,200?

 A: 120

How do I find the total factors of the number 12,421,200?

Step 1

Find the prime factorization of the number 12,421,200.

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

Factor Tree
12,421,200
Factor Arrows
26,210,600
Factor Arrows
23,105,300
Factor Arrows
21,552,650
Factor Arrows
2776,325
Factor Arrows
3258,775
Factor Arrows
551,755
Factor Arrows
510,351
Factor Arrows
11941

The prime factorization in exponential form is: 24 x 31 x 52 x 111 x 9411

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.

12,421,200 = 24 x 31 x 52 x 111 x 9411
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(12421200) = (4 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(12421200) = (5)(2)(3)(2)(2)
Down Arrow
d(12421200) = 120

More numbers for you to try

Take a look at the factors page to see the factors of 12,421,200 and how to find them.

Try the factor calculator.

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