Q: What is the total or count of factors of the number 72,688?

 A: 40

How do I find the total factors of the number 72,688?

Step 1

Find the prime factorization of the number 72,688.

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

Factor Tree
72,688
Factor Arrows
236,344
Factor Arrows
218,172
Factor Arrows
29,086
Factor Arrows
24,543
Factor Arrows
7649
Factor Arrows
1159

The prime factorization in exponential form is: 24 x 71 x 111 x 591

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.

72,688 = 24 x 71 x 111 x 591
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(72688) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(72688) = (5)(2)(2)(2)
Down Arrow
d(72688) = 40

More numbers for you to try

Take a look at the factors page to see the factors of 72,688 and how to find them.

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