Q: What is the total or count of factors of the number 456,489?

 A: 32

How do I find the total factors of the number 456,489?

Step 1

Find the prime factorization of the number 456,489.

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

Factor Tree
456,489
Factor Arrows
3152,163
Factor Arrows
350,721
Factor Arrows
316,907
Factor Arrows
111,537
Factor Arrows
2953

The prime factorization in exponential form is: 33 x 111 x 291 x 531

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.

456,489 = 33 x 111 x 291 x 531
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(456489) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(456489) = (4)(2)(2)(2)
Down Arrow
d(456489) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 456,489 and how to find them.

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