Q: What is the total or count of factors of the number 10,122,408?

 A: 96

How do I find the total factors of the number 10,122,408?

Step 1

Find the prime factorization of the number 10,122,408.

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

Factor Tree
10,122,408
Factor Arrows
25,061,204
Factor Arrows
22,530,602
Factor Arrows
21,265,301
Factor Arrows
3421,767
Factor Arrows
3140,589
Factor Arrows
346,863
Factor Arrows
315,621
Factor Arrows
35,207
Factor Arrows
41127

The prime factorization in exponential form is: 23 x 35 x 411 x 1271

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.

10,122,408 = 23 x 35 x 411 x 1271
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(10122408) = (3 + 1)(5 + 1)(1 + 1)(1 + 1)
Down Arrow
d(10122408) = (4)(6)(2)(2)
Down Arrow
d(10122408) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 10,122,408 and how to find them.

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