Q: What is the total or count of factors of the number 14,954,400?

 A: 216

How do I find the total factors of the number 14,954,400?

Step 1

Find the prime factorization of the number 14,954,400.

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

Factor Tree
14,954,400
Factor Arrows
27,477,200
Factor Arrows
23,738,600
Factor Arrows
21,869,300
Factor Arrows
2934,650
Factor Arrows
2467,325
Factor Arrows
3155,775
Factor Arrows
351,925
Factor Arrows
510,385
Factor Arrows
52,077
Factor Arrows
3167

The prime factorization in exponential form is: 25 x 32 x 52 x 311 x 671

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.

14,954,400 = 25 x 32 x 52 x 311 x 671
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(14954400) = (5 + 1)(2 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(14954400) = (6)(3)(3)(2)(2)
Down Arrow
d(14954400) = 216

More numbers for you to try

Take a look at the factors page to see the factors of 14,954,400 and how to find them.

Try the factor calculator.

Explore more about the number 14,954,400:


Ask a Question