Q: What is the total or count of factors of the number 212,140,560?

 A: 80

How do I find the total factors of the number 212,140,560?

Step 1

Find the prime factorization of the number 212,140,560.

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

Factor Tree
212,140,560
Factor Arrows
2106,070,280
Factor Arrows
253,035,140
Factor Arrows
226,517,570
Factor Arrows
213,258,785
Factor Arrows
34,419,595
Factor Arrows
5883,919
Factor Arrows
4121,559

The prime factorization in exponential form is: 24 x 31 x 51 x 411 x 21,5591

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.

212,140,560 = 24 x 31 x 51 x 411 x 21,5591
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(212140560) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(212140560) = (5)(2)(2)(2)(2)
Down Arrow
d(212140560) = 80

More numbers for you to try

Take a look at the factors page to see the factors of 212,140,560 and how to find them.

Try the factor calculator.

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