Q: What is the total or count of factors of the number 990?

 A: 24

How do I find the total factors of the number 990?

Step 1

Find the prime factorization of the number 990.

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

Factor Tree
990
Factor Arrows
2495
Factor Arrows
3165
Factor Arrows
355
Factor Arrows
511

The prime factorization in exponential form is: 21 x 32 x 51 x 111

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.

990 = 21 x 32 x 51 x 111
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(990) = (1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(990) = (2)(3)(2)(2)
Down Arrow
d(990) = 24

More numbers for you to try

Take a look at the factors page to see the factors of 990 and how to find them.

Try the factor calculator.

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