Q: What is the total or count of factors of the number 23,874,102?

 A: 80

How do I find the total factors of the number 23,874,102?

Step 1

Find the prime factorization of the number 23,874,102.

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

Factor Tree
23,874,102
Factor Arrows
211,937,051
Factor Arrows
33,979,017
Factor Arrows
31,326,339
Factor Arrows
3442,113
Factor Arrows
3147,371
Factor Arrows
721,053
Factor Arrows
37569

The prime factorization in exponential form is: 21 x 34 x 71 x 371 x 5691

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.

23,874,102 = 21 x 34 x 71 x 371 x 5691
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(23874102) = (1 + 1)(4 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(23874102) = (2)(5)(2)(2)(2)
Down Arrow
d(23874102) = 80

More numbers for you to try

Take a look at the factors page to see the factors of 23,874,102 and how to find them.

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