Q: What is the total or count of factors of the number 260,642,400?

 A: 144

How do I find the total factors of the number 260,642,400?

Step 1

Find the prime factorization of the number 260,642,400.

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

Factor Tree
260,642,400
Factor Arrows
2130,321,200
Factor Arrows
265,160,600
Factor Arrows
232,580,300
Factor Arrows
216,290,150
Factor Arrows
28,145,075
Factor Arrows
32,715,025
Factor Arrows
5543,005
Factor Arrows
5108,601
Factor Arrows
223487

The prime factorization in exponential form is: 25 x 31 x 52 x 2231 x 4871

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.

260,642,400 = 25 x 31 x 52 x 2231 x 4871
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(260642400) = (5 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(260642400) = (6)(2)(3)(2)(2)
Down Arrow
d(260642400) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 260,642,400 and how to find them.

Try the factor calculator.

Explore more about the number 260,642,400:


Ask a Question