Q: What is the total or count of factors of the number 200,160?

 A: 72

How do I find the total factors of the number 200,160?

Step 1

Find the prime factorization of the number 200,160.

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

Factor Tree
200,160
Factor Arrows
2100,080
Factor Arrows
250,040
Factor Arrows
225,020
Factor Arrows
212,510
Factor Arrows
26,255
Factor Arrows
32,085
Factor Arrows
3695
Factor Arrows
5139

The prime factorization in exponential form is: 25 x 32 x 51 x 1391

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)

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.

200,160 = 25 x 32 x 51 x 1391
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(200160) = (5 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(200160) = (6)(3)(2)(2)
Down Arrow
d(200160) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 200,160 and how to find them.

Try the factor calculator.

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