Q: What is the total or count of factors of the number 130,152,308?

 A: 72

How do I find the total factors of the number 130,152,308?

Step 1

Find the prime factorization of the number 130,152,308.

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

Factor Tree
130,152,308
Factor Arrows
265,076,154
Factor Arrows
232,538,077
Factor Arrows
112,958,007
Factor Arrows
13227,539
Factor Arrows
1317,503
Factor Arrows
23761

The prime factorization in exponential form is: 22 x 111 x 132 x 231 x 7611

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.

130,152,308 = 22 x 111 x 132 x 231 x 7611
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(130152308) = (2 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(130152308) = (3)(2)(3)(2)(2)
Down Arrow
d(130152308) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 130,152,308 and how to find them.

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