Q: What is the total or count of factors of the number 196,960?

 A: 24

How do I find the total factors of the number 196,960?

Step 1

Find the prime factorization of the number 196,960.

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

Factor Tree
196,960
Factor Arrows
298,480
Factor Arrows
249,240
Factor Arrows
224,620
Factor Arrows
212,310
Factor Arrows
26,155
Factor Arrows
51,231

The prime factorization in exponential form is: 25 x 51 x 1,2311

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 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.

196,960 = 25 x 51 x 1,2311
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(196960) = (5 + 1)(1 + 1)(1 + 1)
Down Arrow
d(196960) = (6)(2)(2)
Down Arrow
d(196960) = 24

More numbers for you to try

Take a look at the factors page to see the factors of 196,960 and how to find them.

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