Q: What is the total or count of factors of the number 277,131,072?

 A: 112

How do I find the total factors of the number 277,131,072?

Step 1

Find the prime factorization of the number 277,131,072.

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

Factor Tree
277,131,072
Factor Arrows
2138,565,536
Factor Arrows
269,282,768
Factor Arrows
234,641,384
Factor Arrows
217,320,692
Factor Arrows
28,660,346
Factor Arrows
24,330,173
Factor Arrows
31,443,391
Factor Arrows
3146,561
Factor Arrows
101461

The prime factorization in exponential form is: 26 x 31 x 311 x 1011 x 4611

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.

277,131,072 = 26 x 31 x 311 x 1011 x 4611
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(277131072) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(277131072) = (7)(2)(2)(2)(2)
Down Arrow
d(277131072) = 112

More numbers for you to try

Take a look at the factors page to see the factors of 277,131,072 and how to find them.

Try the factor calculator.

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