Q: What is the total or count of factors of the number 761,816,736?

 A: 144

How do I find the total factors of the number 761,816,736?

Step 1

Find the prime factorization of the number 761,816,736.

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

Factor Tree
761,816,736
Factor Arrows
2380,908,368
Factor Arrows
2190,454,184
Factor Arrows
295,227,092
Factor Arrows
247,613,546
Factor Arrows
223,806,773
Factor Arrows
37,935,591
Factor Arrows
32,645,197
Factor Arrows
4164,517
Factor Arrows
149433

The prime factorization in exponential form is: 25 x 32 x 411 x 1491 x 4331

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.

761,816,736 = 25 x 32 x 411 x 1491 x 4331
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(761816736) = (5 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(761816736) = (6)(3)(2)(2)(2)
Down Arrow
d(761816736) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 761,816,736 and how to find them.

Try the factor calculator.

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