Q: What is the total or count of factors of the number 123,052,176?

 A: 80

How do I find the total factors of the number 123,052,176?

Step 1

Find the prime factorization of the number 123,052,176.

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

Factor Tree
123,052,176
Factor Arrows
261,526,088
Factor Arrows
230,763,044
Factor Arrows
215,381,522
Factor Arrows
27,690,761
Factor Arrows
32,563,587
Factor Arrows
3854,529
Factor Arrows
3284,843
Factor Arrows
1321,911

The prime factorization in exponential form is: 24 x 33 x 131 x 21,9111

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.

123,052,176 = 24 x 33 x 131 x 21,9111
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(123052176) = (4 + 1)(3 + 1)(1 + 1)(1 + 1)
Down Arrow
d(123052176) = (5)(4)(2)(2)
Down Arrow
d(123052176) = 80

More numbers for you to try

Take a look at the factors page to see the factors of 123,052,176 and how to find them.

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