Q: What is the total or count of factors of the number 187,824?

 A: 80

How do I find the total factors of the number 187,824?

Step 1

Find the prime factorization of the number 187,824.

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

Factor Tree
187,824
Factor Arrows
293,912
Factor Arrows
246,956
Factor Arrows
223,478
Factor Arrows
211,739
Factor Arrows
33,913
Factor Arrows
7559
Factor Arrows
1343

The prime factorization in exponential form is: 24 x 31 x 71 x 131 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)(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.

187,824 = 24 x 31 x 71 x 131 x 431
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(187824) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(187824) = (5)(2)(2)(2)(2)
Down Arrow
d(187824) = 80

More numbers for you to try

Take a look at the factors page to see the factors of 187,824 and how to find them.

Try the factor calculator.

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