Q: What is the total or count of factors of the number 454,431,510?

 A: 48

How do I find the total factors of the number 454,431,510?

Step 1

Find the prime factorization of the number 454,431,510.

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

Factor Tree
454,431,510
Factor Arrows
2227,215,755
Factor Arrows
375,738,585
Factor Arrows
325,246,195
Factor Arrows
55,049,239
Factor Arrows
13388,403

The prime factorization in exponential form is: 21 x 32 x 51 x 131 x 388,4031

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.

454,431,510 = 21 x 32 x 51 x 131 x 388,4031
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(454431510) = (1 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(454431510) = (2)(3)(2)(2)(2)
Down Arrow
d(454431510) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 454,431,510 and how to find them.

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