Q: What is the total or count of factors of the number 354,004,000?

 A: 192

How do I find the total factors of the number 354,004,000?

Step 1

Find the prime factorization of the number 354,004,000.

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

Factor Tree
354,004,000
Factor Arrows
2177,002,000
Factor Arrows
288,501,000
Factor Arrows
244,250,500
Factor Arrows
222,125,250
Factor Arrows
211,062,625
Factor Arrows
52,212,525
Factor Arrows
5442,505
Factor Arrows
588,501
Factor Arrows
712,643
Factor Arrows
47269

The prime factorization in exponential form is: 25 x 53 x 71 x 471 x 2691

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.

354,004,000 = 25 x 53 x 71 x 471 x 2691
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(354004000) = (5 + 1)(3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(354004000) = (6)(4)(2)(2)(2)
Down Arrow
d(354004000) = 192

More numbers for you to try

Take a look at the factors page to see the factors of 354,004,000 and how to find them.

Try the factor calculator.

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