Q: What is the total or count of factors of the number 35,805?

 A: 32

How do I find the total factors of the number 35,805?

Step 1

Find the prime factorization of the number 35,805.

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

Factor Tree
35,805
Factor Arrows
311,935
Factor Arrows
52,387
Factor Arrows
7341
Factor Arrows
1131

The prime factorization in exponential form is: 31 x 51 x 71 x 111 x 311

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.

35,805 = 31 x 51 x 71 x 111 x 311
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(35805) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(35805) = (2)(2)(2)(2)(2)
Down Arrow
d(35805) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 35,805 and how to find them.

Try the factor calculator.

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