Q: What is the total or count of factors of the number 29,876,616?

 A: 192

How do I find the total factors of the number 29,876,616?

Step 1

Find the prime factorization of the number 29,876,616.

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

Factor Tree
29,876,616
Factor Arrows
214,938,308
Factor Arrows
27,469,154
Factor Arrows
23,734,577
Factor Arrows
31,244,859
Factor Arrows
3414,953
Factor Arrows
759,279
Factor Arrows
115,389
Factor Arrows
17317

The prime factorization in exponential form is: 23 x 32 x 71 x 111 x 171 x 3171

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)(f + 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.

29,876,616 = 23 x 32 x 71 x 111 x 171 x 3171
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(29876616) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(29876616) = (4)(3)(2)(2)(2)(2)
Down Arrow
d(29876616) = 192

More numbers for you to try

Take a look at the factors page to see the factors of 29,876,616 and how to find them.

Try the factor calculator.

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