Q: What is the total or count of factors of the number 701,408,736?

 A: 216

How do I find the total factors of the number 701,408,736?

Step 1

Find the prime factorization of the number 701,408,736.

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

Factor Tree
701,408,736
Factor Arrows
2350,704,368
Factor Arrows
2175,352,184
Factor Arrows
287,676,092
Factor Arrows
243,838,046
Factor Arrows
221,919,023
Factor Arrows
37,306,341
Factor Arrows
32,435,447
Factor Arrows
7347,921
Factor Arrows
749,703
Factor Arrows
232,161

The prime factorization in exponential form is: 25 x 32 x 72 x 231 x 2,1611

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.

701,408,736 = 25 x 32 x 72 x 231 x 2,1611
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(701408736) = (5 + 1)(2 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(701408736) = (6)(3)(3)(2)(2)
Down Arrow
d(701408736) = 216

More numbers for you to try

Take a look at the factors page to see the factors of 701,408,736 and how to find them.

Try the factor calculator.

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