Q: What is the total or count of factors of the number 16,114,560?

 A: 256

How do I find the total factors of the number 16,114,560?

Step 1

Find the prime factorization of the number 16,114,560.

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

Factor Tree
16,114,560
Factor Arrows
28,057,280
Factor Arrows
24,028,640
Factor Arrows
22,014,320
Factor Arrows
21,007,160
Factor Arrows
2503,580
Factor Arrows
2251,790
Factor Arrows
2125,895
Factor Arrows
341,965
Factor Arrows
58,393
Factor Arrows
71,199
Factor Arrows
11109

The prime factorization in exponential form is: 27 x 31 x 51 x 71 x 111 x 1091

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.

16,114,560 = 27 x 31 x 51 x 71 x 111 x 1091
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(16114560) = (7 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(16114560) = (8)(2)(2)(2)(2)(2)
Down Arrow
d(16114560) = 256

More numbers for you to try

Take a look at the factors page to see the factors of 16,114,560 and how to find them.

Try the factor calculator.

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