Q: What is the total or count of factors of the number 14,240,512?

 A: 72

How do I find the total factors of the number 14,240,512?

Step 1

Find the prime factorization of the number 14,240,512.

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

Factor Tree
14,240,512
Factor Arrows
27,120,256
Factor Arrows
23,560,128
Factor Arrows
21,780,064
Factor Arrows
2890,032
Factor Arrows
2445,016
Factor Arrows
2222,508
Factor Arrows
2111,254
Factor Arrows
255,627
Factor Arrows
115,057
Factor Arrows
13389

The prime factorization in exponential form is: 28 x 111 x 131 x 3891

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.

14,240,512 = 28 x 111 x 131 x 3891
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(14240512) = (8 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(14240512) = (9)(2)(2)(2)
Down Arrow
d(14240512) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 14,240,512 and how to find them.

Try the factor calculator.

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