Q: What is the total or count of factors of the number 164,496?

 A: 40

How do I find the total factors of the number 164,496?

Step 1

Find the prime factorization of the number 164,496.

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

Factor Tree
164,496
Factor Arrows
282,248
Factor Arrows
241,124
Factor Arrows
220,562
Factor Arrows
210,281
Factor Arrows
33,427
Factor Arrows
23149

The prime factorization in exponential form is: 24 x 31 x 231 x 1491

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.

164,496 = 24 x 31 x 231 x 1491
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(164496) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(164496) = (5)(2)(2)(2)
Down Arrow
d(164496) = 40

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Take a look at the factors page to see the factors of 164,496 and how to find them.

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