Q: What is the total or count of factors of the number 150,085,760?

 A: 64

How do I find the total factors of the number 150,085,760?

Step 1

Find the prime factorization of the number 150,085,760.

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

Factor Tree
150,085,760
Factor Arrows
275,042,880
Factor Arrows
237,521,440
Factor Arrows
218,760,720
Factor Arrows
29,380,360
Factor Arrows
24,690,180
Factor Arrows
22,345,090
Factor Arrows
21,172,545
Factor Arrows
5234,509
Factor Arrows
1121,319

The prime factorization in exponential form is: 27 x 51 x 111 x 21,3191

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.

150,085,760 = 27 x 51 x 111 x 21,3191
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(150085760) = (7 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(150085760) = (8)(2)(2)(2)
Down Arrow
d(150085760) = 64

More numbers for you to try

Take a look at the factors page to see the factors of 150,085,760 and how to find them.

Try the factor calculator.

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