Q: What is the total or count of factors of the number 207,050,140?

 A: 192

How do I find the total factors of the number 207,050,140?

Step 1

Find the prime factorization of the number 207,050,140.

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

Factor Tree
207,050,140
Factor Arrows
2103,525,070
Factor Arrows
251,762,535
Factor Arrows
510,352,507
Factor Arrows
11941,137
Factor Arrows
1755,361
Factor Arrows
232,407
Factor Arrows
2983

The prime factorization in exponential form is: 22 x 51 x 111 x 171 x 231 x 291 x 831

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)(f + 1)(g + 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.

207,050,140 = 22 x 51 x 111 x 171 x 231 x 291 x 831
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)(g + 1)
Down Arrow
d(207050140) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(207050140) = (3)(2)(2)(2)(2)(2)(2)
Down Arrow
d(207050140) = 192

More numbers for you to try

Take a look at the factors page to see the factors of 207,050,140 and how to find them.

Try the factor calculator.

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