Q: What is the total or count of factors of the number 160,896?

 A: 32

How do I find the total factors of the number 160,896?

Step 1

Find the prime factorization of the number 160,896.

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

Factor Tree
160,896
Factor Arrows
280,448
Factor Arrows
240,224
Factor Arrows
220,112
Factor Arrows
210,056
Factor Arrows
25,028
Factor Arrows
22,514
Factor Arrows
21,257
Factor Arrows
3419

The prime factorization in exponential form is: 27 x 31 x 4191

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.

160,896 = 27 x 31 x 4191
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(160896) = (7 + 1)(1 + 1)(1 + 1)
Down Arrow
d(160896) = (8)(2)(2)
Down Arrow
d(160896) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 160,896 and how to find them.

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