Q: What is the total or count of factors of the number 177,660?

 A: 96

How do I find the total factors of the number 177,660?

Step 1

Find the prime factorization of the number 177,660.

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

Factor Tree
177,660
Factor Arrows
288,830
Factor Arrows
244,415
Factor Arrows
314,805
Factor Arrows
34,935
Factor Arrows
31,645
Factor Arrows
5329
Factor Arrows
747

The prime factorization in exponential form is: 22 x 33 x 51 x 71 x 471

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)(e + 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.

177,660 = 22 x 33 x 51 x 71 x 471
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(177660) = (2 + 1)(3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(177660) = (3)(4)(2)(2)(2)
Down Arrow
d(177660) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 177,660 and how to find them.

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