Q: What is the total or count of factors of the number 1,282,204?

 A: 48

How do I find the total factors of the number 1,282,204?

Step 1

Find the prime factorization of the number 1,282,204.

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

Factor Tree
1,282,204
Factor Arrows
2641,102
Factor Arrows
2320,551
Factor Arrows
745,793
Factor Arrows
114,163
Factor Arrows
23181

The prime factorization in exponential form is: 22 x 71 x 111 x 231 x 1811

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.

1,282,204 = 22 x 71 x 111 x 231 x 1811
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(1282204) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(1282204) = (3)(2)(2)(2)(2)
Down Arrow
d(1282204) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 1,282,204 and how to find them.

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