Q: What is the total or count of factors of the number 224,021,140?

 A: 36

How do I find the total factors of the number 224,021,140?

Step 1

Find the prime factorization of the number 224,021,140.

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

Factor Tree
224,021,140
Factor Arrows
2112,010,570
Factor Arrows
256,005,285
Factor Arrows
511,201,057
Factor Arrows
71,600,151
Factor Arrows
7228,593

The prime factorization in exponential form is: 22 x 51 x 72 x 228,5931

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.

224,021,140 = 22 x 51 x 72 x 228,5931
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(224021140) = (2 + 1)(1 + 1)(2 + 1)(1 + 1)
Down Arrow
d(224021140) = (3)(2)(3)(2)
Down Arrow
d(224021140) = 36

More numbers for you to try

Take a look at the factors page to see the factors of 224,021,140 and how to find them.

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