Q: What is the total or count of factors of the number 34,801,728?

 A: 112

How do I find the total factors of the number 34,801,728?

Step 1

Find the prime factorization of the number 34,801,728.

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

Factor Tree
34,801,728
Factor Arrows
217,400,864
Factor Arrows
28,700,432
Factor Arrows
24,350,216
Factor Arrows
22,175,108
Factor Arrows
21,087,554
Factor Arrows
2543,777
Factor Arrows
3181,259
Factor Arrows
1313,943
Factor Arrows
73191

The prime factorization in exponential form is: 26 x 31 x 131 x 731 x 1911

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.

34,801,728 = 26 x 31 x 131 x 731 x 1911
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(34801728) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(34801728) = (7)(2)(2)(2)(2)
Down Arrow
d(34801728) = 112

More numbers for you to try

Take a look at the factors page to see the factors of 34,801,728 and how to find them.

Try the factor calculator.

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