Q: What is the total or count of factors of the number 322,332,048?

 A: 200

How do I find the total factors of the number 322,332,048?

Step 1

Find the prime factorization of the number 322,332,048.

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

Factor Tree
322,332,048
Factor Arrows
2161,166,024
Factor Arrows
280,583,012
Factor Arrows
240,291,506
Factor Arrows
220,145,753
Factor Arrows
36,715,251
Factor Arrows
32,238,417
Factor Arrows
3746,139
Factor Arrows
3248,713
Factor Arrows
318,023
Factor Arrows
71113

The prime factorization in exponential form is: 24 x 34 x 311 x 711 x 1131

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.

322,332,048 = 24 x 34 x 311 x 711 x 1131
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(322332048) = (4 + 1)(4 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(322332048) = (5)(5)(2)(2)(2)
Down Arrow
d(322332048) = 200

More numbers for you to try

Take a look at the factors page to see the factors of 322,332,048 and how to find them.

Try the factor calculator.

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