Q: What is the total or count of factors of the number 712,653,201?

 A: 32

How do I find the total factors of the number 712,653,201?

Step 1

Find the prime factorization of the number 712,653,201.

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

Factor Tree
712,653,201
Factor Arrows
3237,551,067
Factor Arrows
379,183,689
Factor Arrows
326,394,563
Factor Arrows
132,030,351
Factor Arrows
1,0911,861

The prime factorization in exponential form is: 33 x 131 x 1,0911 x 1,8611

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)

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.

712,653,201 = 33 x 131 x 1,0911 x 1,8611
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(712653201) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(712653201) = (4)(2)(2)(2)
Down Arrow
d(712653201) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 712,653,201 and how to find them.

Try the factor calculator.

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