Q: What is the total or count of factors of the number 15,165,648?

 A: 120

How do I find the total factors of the number 15,165,648?

Step 1

Find the prime factorization of the number 15,165,648.

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

Factor Tree
15,165,648
Factor Arrows
27,582,824
Factor Arrows
23,791,412
Factor Arrows
21,895,706
Factor Arrows
2947,853
Factor Arrows
3315,951
Factor Arrows
3105,317
Factor Arrows
195,543
Factor Arrows
23241

The prime factorization in exponential form is: 24 x 32 x 191 x 231 x 2411

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.

15,165,648 = 24 x 32 x 191 x 231 x 2411
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(15165648) = (4 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(15165648) = (5)(3)(2)(2)(2)
Down Arrow
d(15165648) = 120

More numbers for you to try

Take a look at the factors page to see the factors of 15,165,648 and how to find them.

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