Q: What is the total or count of factors of the number 5,821,200?

 A: 360

How do I find the total factors of the number 5,821,200?

Step 1

Find the prime factorization of the number 5,821,200.

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

Factor Tree
5,821,200
Factor Arrows
22,910,600
Factor Arrows
21,455,300
Factor Arrows
2727,650
Factor Arrows
2363,825
Factor Arrows
3121,275
Factor Arrows
340,425
Factor Arrows
313,475
Factor Arrows
52,695
Factor Arrows
5539
Factor Arrows
777
Factor Arrows
711

The prime factorization in exponential form is: 24 x 33 x 52 x 72 x 111

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.

5,821,200 = 24 x 33 x 52 x 72 x 111
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(5821200) = (4 + 1)(3 + 1)(2 + 1)(2 + 1)(1 + 1)
Down Arrow
d(5821200) = (5)(4)(3)(3)(2)
Down Arrow
d(5821200) = 360

More numbers for you to try

Take a look at the factors page to see the factors of 5,821,200 and how to find them.

Try the factor calculator.

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