Q: What is the total or count of factors of the number 506,464,112?

 A: 160

How do I find the total factors of the number 506,464,112?

Step 1

Find the prime factorization of the number 506,464,112.

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

Factor Tree
506,464,112
Factor Arrows
2253,232,056
Factor Arrows
2126,616,028
Factor Arrows
263,308,014
Factor Arrows
231,654,007
Factor Arrows
74,522,001
Factor Arrows
11411,091
Factor Arrows
3113,261
Factor Arrows
89149

The prime factorization in exponential form is: 24 x 71 x 111 x 311 x 891 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)(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.

506,464,112 = 24 x 71 x 111 x 311 x 891 x 1491
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(506464112) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(506464112) = (5)(2)(2)(2)(2)(2)
Down Arrow
d(506464112) = 160

More numbers for you to try

Take a look at the factors page to see the factors of 506,464,112 and how to find them.

Try the factor calculator.

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