Q: What is the total or count of factors of the number 312,021,126?

 A: 32

How do I find the total factors of the number 312,021,126?

Step 1

Find the prime factorization of the number 312,021,126.

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

Factor Tree
312,021,126
Factor Arrows
2156,010,563
Factor Arrows
352,003,521
Factor Arrows
317,334,507
Factor Arrows
35,778,169
Factor Arrows
7379,153

The prime factorization in exponential form is: 21 x 33 x 731 x 79,1531

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.

312,021,126 = 21 x 33 x 731 x 79,1531
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(312021126) = (1 + 1)(3 + 1)(1 + 1)(1 + 1)
Down Arrow
d(312021126) = (2)(4)(2)(2)
Down Arrow
d(312021126) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 312,021,126 and how to find them.

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