Q: What is the total or count of factors of the number 33,102,672?

 A: 80

How do I find the total factors of the number 33,102,672?

Step 1

Find the prime factorization of the number 33,102,672.

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

Factor Tree
33,102,672
Factor Arrows
216,551,336
Factor Arrows
28,275,668
Factor Arrows
24,137,834
Factor Arrows
22,068,917
Factor Arrows
3689,639
Factor Arrows
1740,567
Factor Arrows
113359

The prime factorization in exponential form is: 24 x 31 x 171 x 1131 x 3591

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.

33,102,672 = 24 x 31 x 171 x 1131 x 3591
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(33102672) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(33102672) = (5)(2)(2)(2)(2)
Down Arrow
d(33102672) = 80

More numbers for you to try

Take a look at the factors page to see the factors of 33,102,672 and how to find them.

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