Q: What is the total or count of factors of the number 312,213,750?

 A: 40

How do I find the total factors of the number 312,213,750?

Step 1

Find the prime factorization of the number 312,213,750.

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

Factor Tree
312,213,750
Factor Arrows
2156,106,875
Factor Arrows
352,035,625
Factor Arrows
510,407,125
Factor Arrows
52,081,425
Factor Arrows
5416,285
Factor Arrows
583,257

The prime factorization in exponential form is: 21 x 31 x 54 x 83,2571

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.

312,213,750 = 21 x 31 x 54 x 83,2571
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(312213750) = (1 + 1)(1 + 1)(4 + 1)(1 + 1)
Down Arrow
d(312213750) = (2)(2)(5)(2)
Down Arrow
d(312213750) = 40

More numbers for you to try

Take a look at the factors page to see the factors of 312,213,750 and how to find them.

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