Q: What is the total or count of factors of the number 267,890?

 A: 32

How do I find the total factors of the number 267,890?

Step 1

Find the prime factorization of the number 267,890.

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

Factor Tree
267,890
Factor Arrows
2133,945
Factor Arrows
526,789
Factor Arrows
73,827
Factor Arrows
4389

The prime factorization in exponential form is: 21 x 51 x 71 x 431 x 891

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.

267,890 = 21 x 51 x 71 x 431 x 891
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(267890) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(267890) = (2)(2)(2)(2)(2)
Down Arrow
d(267890) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 267,890 and how to find them.

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