Q: What is the total or count of factors of the number 14,659,600?

 A: 60

How do I find the total factors of the number 14,659,600?

Step 1

Find the prime factorization of the number 14,659,600.

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

Factor Tree
14,659,600
Factor Arrows
27,329,800
Factor Arrows
23,664,900
Factor Arrows
21,832,450
Factor Arrows
2916,225
Factor Arrows
5183,245
Factor Arrows
536,649
Factor Arrows
67547

The prime factorization in exponential form is: 24 x 52 x 671 x 5471

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.

14,659,600 = 24 x 52 x 671 x 5471
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(14659600) = (4 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(14659600) = (5)(3)(2)(2)
Down Arrow
d(14659600) = 60

More numbers for you to try

Take a look at the factors page to see the factors of 14,659,600 and how to find them.

Try the factor calculator.

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