Q: What is the total or count of factors of the number 351,401,616?

 A: 120

How do I find the total factors of the number 351,401,616?

Step 1

Find the prime factorization of the number 351,401,616.

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

Factor Tree
351,401,616
Factor Arrows
2175,700,808
Factor Arrows
287,850,404
Factor Arrows
243,925,202
Factor Arrows
221,962,601
Factor Arrows
37,320,867
Factor Arrows
32,440,289
Factor Arrows
3178,719
Factor Arrows
223353

The prime factorization in exponential form is: 24 x 32 x 311 x 2231 x 3531

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.

351,401,616 = 24 x 32 x 311 x 2231 x 3531
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(351401616) = (4 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(351401616) = (5)(3)(2)(2)(2)
Down Arrow
d(351401616) = 120

More numbers for you to try

Take a look at the factors page to see the factors of 351,401,616 and how to find them.

Try the factor calculator.

Explore more about the number 351,401,616:


Ask a Question