Q: What is the total or count of factors of the number 403,110,456?

 A: 96

How do I find the total factors of the number 403,110,456?

Step 1

Find the prime factorization of the number 403,110,456.

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

Factor Tree
403,110,456
Factor Arrows
2201,555,228
Factor Arrows
2100,777,614
Factor Arrows
250,388,807
Factor Arrows
316,796,269
Factor Arrows
72,399,467
Factor Arrows
7342,781
Factor Arrows
794,339

The prime factorization in exponential form is: 23 x 31 x 72 x 791 x 4,3391

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.

403,110,456 = 23 x 31 x 72 x 791 x 4,3391
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(403110456) = (3 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(403110456) = (4)(2)(3)(2)(2)
Down Arrow
d(403110456) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 403,110,456 and how to find them.

Try the factor calculator.

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