Q: What is the total or count of factors of the number 8,150,400?

 A: 144

How do I find the total factors of the number 8,150,400?

Step 1

Find the prime factorization of the number 8,150,400.

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

Factor Tree
8,150,400
Factor Arrows
24,075,200
Factor Arrows
22,037,600
Factor Arrows
21,018,800
Factor Arrows
2509,400
Factor Arrows
2254,700
Factor Arrows
2127,350
Factor Arrows
263,675
Factor Arrows
321,225
Factor Arrows
37,075
Factor Arrows
51,415
Factor Arrows
5283

The prime factorization in exponential form is: 27 x 32 x 52 x 2831

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.

8,150,400 = 27 x 32 x 52 x 2831
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(8150400) = (7 + 1)(2 + 1)(2 + 1)(1 + 1)
Down Arrow
d(8150400) = (8)(3)(3)(2)
Down Arrow
d(8150400) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 8,150,400 and how to find them.

Try the factor calculator.

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