Q: What is the total or count of factors of the number 21,310,100?

 A: 54

How do I find the total factors of the number 21,310,100?

Step 1

Find the prime factorization of the number 21,310,100.

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

Factor Tree
21,310,100
Factor Arrows
210,655,050
Factor Arrows
25,327,525
Factor Arrows
51,065,505
Factor Arrows
5213,101
Factor Arrows
730,443
Factor Arrows
74,349

The prime factorization in exponential form is: 22 x 52 x 72 x 4,3491

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)

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.

21,310,100 = 22 x 52 x 72 x 4,3491
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(21310100) = (2 + 1)(2 + 1)(2 + 1)(1 + 1)
Down Arrow
d(21310100) = (3)(3)(3)(2)
Down Arrow
d(21310100) = 54

More numbers for you to try

Take a look at the factors page to see the factors of 21,310,100 and how to find them.

Try the factor calculator.

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