Q: What is the total or count of factors of the number 29,565,648?

 A: 100

How do I find the total factors of the number 29,565,648?

Step 1

Find the prime factorization of the number 29,565,648.

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

Factor Tree
29,565,648
Factor Arrows
214,782,824
Factor Arrows
27,391,412
Factor Arrows
23,695,706
Factor Arrows
21,847,853
Factor Arrows
3615,951
Factor Arrows
3205,317
Factor Arrows
368,439
Factor Arrows
322,813
Factor Arrows
73,259

The prime factorization in exponential form is: 24 x 34 x 71 x 3,2591

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.

29,565,648 = 24 x 34 x 71 x 3,2591
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(29565648) = (4 + 1)(4 + 1)(1 + 1)(1 + 1)
Down Arrow
d(29565648) = (5)(5)(2)(2)
Down Arrow
d(29565648) = 100

More numbers for you to try

Take a look at the factors page to see the factors of 29,565,648 and how to find them.

Try the factor calculator.

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