Q: What is the total or count of factors of the number 531,214,825?

 A: 24

How do I find the total factors of the number 531,214,825?

Step 1

Find the prime factorization of the number 531,214,825.

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

Factor Tree
531,214,825
Factor Arrows
5106,242,965
Factor Arrows
521,248,593
Factor Arrows
191,118,347
Factor Arrows
1318,537

The prime factorization in exponential form is: 52 x 191 x 1311 x 8,5371

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.

531,214,825 = 52 x 191 x 1311 x 8,5371
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(531214825) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(531214825) = (3)(2)(2)(2)
Down Arrow
d(531214825) = 24

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Take a look at the factors page to see the factors of 531,214,825 and how to find them.

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