Q: What is the total or count of factors of the number 214,566?

 A: 16

How do I find the total factors of the number 214,566?

Step 1

Find the prime factorization of the number 214,566.

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

Factor Tree
214,566
Factor Arrows
2107,283
Factor Arrows
335,761
Factor Arrows
113,251

The prime factorization in exponential form is: 21 x 31 x 111 x 3,2511

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.

214,566 = 21 x 31 x 111 x 3,2511
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(214566) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(214566) = (2)(2)(2)(2)
Down Arrow
d(214566) = 16

More numbers for you to try

Take a look at the factors page to see the factors of 214,566 and how to find them.

Try the factor calculator.

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