Q: What is the total or count of factors of the number 165,516,148?

 A: 48

How do I find the total factors of the number 165,516,148?

Step 1

Find the prime factorization of the number 165,516,148.

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

Factor Tree
165,516,148
Factor Arrows
282,758,074
Factor Arrows
241,379,037
Factor Arrows
75,911,291
Factor Arrows
17347,723
Factor Arrows
893,907

The prime factorization in exponential form is: 22 x 71 x 171 x 891 x 3,9071

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.

165,516,148 = 22 x 71 x 171 x 891 x 3,9071
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(165516148) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(165516148) = (3)(2)(2)(2)(2)
Down Arrow
d(165516148) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 165,516,148 and how to find them.

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