Q: What is the total or count of factors of the number 16,585,140?

 A: 96

How do I find the total factors of the number 16,585,140?

Step 1

Find the prime factorization of the number 16,585,140.

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

Factor Tree
16,585,140
Factor Arrows
28,292,570
Factor Arrows
24,146,285
Factor Arrows
31,382,095
Factor Arrows
5276,419
Factor Arrows
1125,129
Factor Arrows
131,933

The prime factorization in exponential form is: 22 x 31 x 51 x 111 x 131 x 1,9331

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)(f + 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.

16,585,140 = 22 x 31 x 51 x 111 x 131 x 1,9331
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(16585140) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(16585140) = (3)(2)(2)(2)(2)(2)
Down Arrow
d(16585140) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 16,585,140 and how to find them.

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