Q: What is the total or count of factors of the number 112,213,220?

 A: 48

How do I find the total factors of the number 112,213,220?

Step 1

Find the prime factorization of the number 112,213,220.

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

Factor Tree
112,213,220
Factor Arrows
256,106,610
Factor Arrows
228,053,305
Factor Arrows
55,610,661
Factor Arrows
7801,523
Factor Arrows
5571,439

The prime factorization in exponential form is: 22 x 51 x 71 x 5571 x 1,4391

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.

112,213,220 = 22 x 51 x 71 x 5571 x 1,4391
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(112213220) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(112213220) = (3)(2)(2)(2)(2)
Down Arrow
d(112213220) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 112,213,220 and how to find them.

Try the factor calculator.

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