Q: What is the total or count of factors of the number 403,152,000?

 A: 256

How do I find the total factors of the number 403,152,000?

Step 1

Find the prime factorization of the number 403,152,000.

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

Factor Tree
403,152,000
Factor Arrows
2201,576,000
Factor Arrows
2100,788,000
Factor Arrows
250,394,000
Factor Arrows
225,197,000
Factor Arrows
212,598,500
Factor Arrows
26,299,250
Factor Arrows
23,149,625
Factor Arrows
31,049,875
Factor Arrows
5209,975
Factor Arrows
541,995
Factor Arrows
58,399
Factor Arrows
37227

The prime factorization in exponential form is: 27 x 31 x 53 x 371 x 2271

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.

403,152,000 = 27 x 31 x 53 x 371 x 2271
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(403152000) = (7 + 1)(1 + 1)(3 + 1)(1 + 1)(1 + 1)
Down Arrow
d(403152000) = (8)(2)(4)(2)(2)
Down Arrow
d(403152000) = 256

More numbers for you to try

Take a look at the factors page to see the factors of 403,152,000 and how to find them.

Try the factor calculator.

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