Q: What is the total or count of factors of the number 21,425,100?

 A: 72

How do I find the total factors of the number 21,425,100?

Step 1

Find the prime factorization of the number 21,425,100.

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

Factor Tree
21,425,100
Factor Arrows
210,712,550
Factor Arrows
25,356,275
Factor Arrows
31,785,425
Factor Arrows
5357,085
Factor Arrows
571,417
Factor Arrows
174,201

The prime factorization in exponential form is: 22 x 31 x 52 x 171 x 4,2011

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.

21,425,100 = 22 x 31 x 52 x 171 x 4,2011
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(21425100) = (2 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(21425100) = (3)(2)(3)(2)(2)
Down Arrow
d(21425100) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 21,425,100 and how to find them.

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