Q: What is the total or count of factors of the number 538,464?

 A: 48

How do I find the total factors of the number 538,464?

Step 1

Find the prime factorization of the number 538,464.

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

Factor Tree
538,464
Factor Arrows
2269,232
Factor Arrows
2134,616
Factor Arrows
267,308
Factor Arrows
233,654
Factor Arrows
216,827
Factor Arrows
35,609
Factor Arrows
7179

The prime factorization in exponential form is: 25 x 31 x 711 x 791

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.

538,464 = 25 x 31 x 711 x 791
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(538464) = (5 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(538464) = (6)(2)(2)(2)
Down Arrow
d(538464) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 538,464 and how to find them.

Try the factor calculator.

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