Q: What is the total or count of factors of the number 232,141,206?

 A: 64

How do I find the total factors of the number 232,141,206?

Step 1

Find the prime factorization of the number 232,141,206.

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

Factor Tree
232,141,206
Factor Arrows
2116,070,603
Factor Arrows
338,690,201
Factor Arrows
113,517,291
Factor Arrows
31113,461
Factor Arrows
831,367

The prime factorization in exponential form is: 21 x 31 x 111 x 311 x 831 x 1,3671

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)(f + 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.

232,141,206 = 21 x 31 x 111 x 311 x 831 x 1,3671
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(232141206) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(232141206) = (2)(2)(2)(2)(2)(2)
Down Arrow
d(232141206) = 64

More numbers for you to try

Take a look at the factors page to see the factors of 232,141,206 and how to find them.

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