Q: What is the total or count of factors of the number 66,051,600?

 A: 120

How do I find the total factors of the number 66,051,600?

Step 1

Find the prime factorization of the number 66,051,600.

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

Factor Tree
66,051,600
Factor Arrows
233,025,800
Factor Arrows
216,512,900
Factor Arrows
28,256,450
Factor Arrows
24,128,225
Factor Arrows
31,376,075
Factor Arrows
5275,215
Factor Arrows
555,043
Factor Arrows
192,897

The prime factorization in exponential form is: 24 x 31 x 52 x 191 x 2,8971

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.

66,051,600 = 24 x 31 x 52 x 191 x 2,8971
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(66051600) = (4 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(66051600) = (5)(2)(3)(2)(2)
Down Arrow
d(66051600) = 120

More numbers for you to try

Take a look at the factors page to see the factors of 66,051,600 and how to find them.

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