Q: What is the total or count of factors of the number 77,227,584?

 A: 112

How do I find the total factors of the number 77,227,584?

Step 1

Find the prime factorization of the number 77,227,584.

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

Factor Tree
77,227,584
Factor Arrows
238,613,792
Factor Arrows
219,306,896
Factor Arrows
29,653,448
Factor Arrows
24,826,724
Factor Arrows
22,413,362
Factor Arrows
21,206,681
Factor Arrows
3402,227
Factor Arrows
757,461
Factor Arrows
371,553

The prime factorization in exponential form is: 26 x 31 x 71 x 371 x 1,5531

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.

77,227,584 = 26 x 31 x 71 x 371 x 1,5531
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(77227584) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(77227584) = (7)(2)(2)(2)(2)
Down Arrow
d(77227584) = 112

More numbers for you to try

Take a look at the factors page to see the factors of 77,227,584 and how to find them.

Try the factor calculator.

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