Q: What is the total or count of factors of the number 37,777,800?

 A: 96

How do I find the total factors of the number 37,777,800?

Step 1

Find the prime factorization of the number 37,777,800.

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

Factor Tree
37,777,800
Factor Arrows
218,888,900
Factor Arrows
29,444,450
Factor Arrows
24,722,225
Factor Arrows
31,574,075
Factor Arrows
5314,815
Factor Arrows
562,963
Factor Arrows
79797

The prime factorization in exponential form is: 23 x 31 x 52 x 791 x 7971

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.

37,777,800 = 23 x 31 x 52 x 791 x 7971
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(37777800) = (3 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(37777800) = (4)(2)(3)(2)(2)
Down Arrow
d(37777800) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 37,777,800 and how to find them.

Try the factor calculator.

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