Q: What is the total or count of factors of the number 34,511,664?

 A: 80

How do I find the total factors of the number 34,511,664?

Step 1

Find the prime factorization of the number 34,511,664.

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

Factor Tree
34,511,664
Factor Arrows
217,255,832
Factor Arrows
28,627,916
Factor Arrows
24,313,958
Factor Arrows
22,156,979
Factor Arrows
3718,993
Factor Arrows
1165,363
Factor Arrows
163401

The prime factorization in exponential form is: 24 x 31 x 111 x 1631 x 4011

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.

34,511,664 = 24 x 31 x 111 x 1631 x 4011
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(34511664) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(34511664) = (5)(2)(2)(2)(2)
Down Arrow
d(34511664) = 80

More numbers for you to try

Take a look at the factors page to see the factors of 34,511,664 and how to find them.

Try the factor calculator.

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