Q: What is the total or count of factors of the number 521,700?

 A: 72

How do I find the total factors of the number 521,700?

Step 1

Find the prime factorization of the number 521,700.

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

Factor Tree
521,700
Factor Arrows
2260,850
Factor Arrows
2130,425
Factor Arrows
343,475
Factor Arrows
58,695
Factor Arrows
51,739
Factor Arrows
3747

The prime factorization in exponential form is: 22 x 31 x 52 x 371 x 471

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)(e + 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.

521,700 = 22 x 31 x 52 x 371 x 471
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(521700) = (2 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(521700) = (3)(2)(3)(2)(2)
Down Arrow
d(521700) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 521,700 and how to find them.

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