Q: What is the total or count of factors of the number 814,592?

 A: 40

How do I find the total factors of the number 814,592?

Step 1

Find the prime factorization of the number 814,592.

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

Factor Tree
814,592
Factor Arrows
2407,296
Factor Arrows
2203,648
Factor Arrows
2101,824
Factor Arrows
250,912
Factor Arrows
225,456
Factor Arrows
212,728
Factor Arrows
26,364
Factor Arrows
23,182
Factor Arrows
21,591
Factor Arrows
3743

The prime factorization in exponential form is: 29 x 371 x 431

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.

814,592 = 29 x 371 x 431
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(814592) = (9 + 1)(1 + 1)(1 + 1)
Down Arrow
d(814592) = (10)(2)(2)
Down Arrow
d(814592) = 40

More numbers for you to try

Take a look at the factors page to see the factors of 814,592 and how to find them.

Try the factor calculator.

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