Q: What is the total or count of factors of the number 21,379,512?

 A: 128

How do I find the total factors of the number 21,379,512?

Step 1

Find the prime factorization of the number 21,379,512.

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

Factor Tree
21,379,512
Factor Arrows
210,689,756
Factor Arrows
25,344,878
Factor Arrows
22,672,439
Factor Arrows
3890,813
Factor Arrows
7127,259
Factor Arrows
1111,569
Factor Arrows
23503

The prime factorization in exponential form is: 23 x 31 x 71 x 111 x 231 x 5031

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.

21,379,512 = 23 x 31 x 71 x 111 x 231 x 5031
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(21379512) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(21379512) = (4)(2)(2)(2)(2)(2)
Down Arrow
d(21379512) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 21,379,512 and how to find them.

Try the factor calculator.

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