Q: What is the total or count of factors of the number 83,312,220?

 A: 48

How do I find the total factors of the number 83,312,220?

Step 1

Find the prime factorization of the number 83,312,220.

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

Factor Tree
83,312,220
Factor Arrows
241,656,110
Factor Arrows
220,828,055
Factor Arrows
36,942,685
Factor Arrows
51,388,537
Factor Arrows
4632,999

The prime factorization in exponential form is: 22 x 31 x 51 x 4631 x 2,9991

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.

83,312,220 = 22 x 31 x 51 x 4631 x 2,9991
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(83312220) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(83312220) = (3)(2)(2)(2)(2)
Down Arrow
d(83312220) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 83,312,220 and how to find them.

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