Q: What is the total or count of factors of the number 34,387,056?

 A: 120

How do I find the total factors of the number 34,387,056?

Step 1

Find the prime factorization of the number 34,387,056.

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

Factor Tree
34,387,056
Factor Arrows
217,193,528
Factor Arrows
28,596,764
Factor Arrows
24,298,382
Factor Arrows
22,149,191
Factor Arrows
3716,397
Factor Arrows
3238,799
Factor Arrows
1121,709
Factor Arrows
171,277

The prime factorization in exponential form is: 24 x 32 x 111 x 171 x 1,2771

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.

34,387,056 = 24 x 32 x 111 x 171 x 1,2771
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(34387056) = (4 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(34387056) = (5)(3)(2)(2)(2)
Down Arrow
d(34387056) = 120

More numbers for you to try

Take a look at the factors page to see the factors of 34,387,056 and how to find them.

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