Q: What is the total or count of factors of the number 102,600?

 A: 96

How do I find the total factors of the number 102,600?

Step 1

Find the prime factorization of the number 102,600.

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

Factor Tree
102,600
Factor Arrows
251,300
Factor Arrows
225,650
Factor Arrows
212,825
Factor Arrows
34,275
Factor Arrows
31,425
Factor Arrows
3475
Factor Arrows
595
Factor Arrows
519

The prime factorization in exponential form is: 23 x 33 x 52 x 191

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.

102,600 = 23 x 33 x 52 x 191
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(102600) = (3 + 1)(3 + 1)(2 + 1)(1 + 1)
Down Arrow
d(102600) = (4)(4)(3)(2)
Down Arrow
d(102600) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 102,600 and how to find them.

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