Q: What is the total or count of factors of the number 830,900?

 A: 36

How do I find the total factors of the number 830,900?

Step 1

Find the prime factorization of the number 830,900.

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

Factor Tree
830,900
Factor Arrows
2415,450
Factor Arrows
2207,725
Factor Arrows
541,545
Factor Arrows
58,309
Factor Arrows
71,187

The prime factorization in exponential form is: 22 x 52 x 71 x 1,1871

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)

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.

830,900 = 22 x 52 x 71 x 1,1871
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(830900) = (2 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(830900) = (3)(3)(2)(2)
Down Arrow
d(830900) = 36

More numbers for you to try

Take a look at the factors page to see the factors of 830,900 and how to find them.

Try the factor calculator.

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