Q: What is the total or count of factors of the number 409,120?

 A: 24

How do I find the total factors of the number 409,120?

Step 1

Find the prime factorization of the number 409,120.

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

Factor Tree
409,120
Factor Arrows
2204,560
Factor Arrows
2102,280
Factor Arrows
251,140
Factor Arrows
225,570
Factor Arrows
212,785
Factor Arrows
52,557

The prime factorization in exponential form is: 25 x 51 x 2,5571

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 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.

409,120 = 25 x 51 x 2,5571
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(409120) = (5 + 1)(1 + 1)(1 + 1)
Down Arrow
d(409120) = (6)(2)(2)
Down Arrow
d(409120) = 24

More numbers for you to try

Take a look at the factors page to see the factors of 409,120 and how to find them.

Try the factor calculator.

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