Q: What is the total or count of factors of the number 3,278,100?

 A: 108

How do I find the total factors of the number 3,278,100?

Step 1

Find the prime factorization of the number 3,278,100.

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

Factor Tree
3,278,100
Factor Arrows
21,639,050
Factor Arrows
2819,525
Factor Arrows
3273,175
Factor Arrows
554,635
Factor Arrows
510,927
Factor Arrows
71,561
Factor Arrows
7223

The prime factorization in exponential form is: 22 x 31 x 52 x 72 x 2231

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.

3,278,100 = 22 x 31 x 52 x 72 x 2231
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(3278100) = (2 + 1)(1 + 1)(2 + 1)(2 + 1)(1 + 1)
Down Arrow
d(3278100) = (3)(2)(3)(3)(2)
Down Arrow
d(3278100) = 108

More numbers for you to try

Take a look at the factors page to see the factors of 3,278,100 and how to find them.

Try the factor calculator.

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