Q: What is the total or count of factors of the number 155,904?

 A: 72

How do I find the total factors of the number 155,904?

Step 1

Find the prime factorization of the number 155,904.

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

Factor Tree
155,904
Factor Arrows
277,952
Factor Arrows
238,976
Factor Arrows
219,488
Factor Arrows
29,744
Factor Arrows
24,872
Factor Arrows
22,436
Factor Arrows
21,218
Factor Arrows
2609
Factor Arrows
3203
Factor Arrows
729

The prime factorization in exponential form is: 28 x 31 x 71 x 291

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.

155,904 = 28 x 31 x 71 x 291
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(155904) = (8 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(155904) = (9)(2)(2)(2)
Down Arrow
d(155904) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 155,904 and how to find them.

Try the factor calculator.

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