Q: What is the total or count of factors of the number 245,140,160?

 A: 56

How do I find the total factors of the number 245,140,160?

Step 1

Find the prime factorization of the number 245,140,160.

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

Factor Tree
245,140,160
Factor Arrows
2122,570,080
Factor Arrows
261,285,040
Factor Arrows
230,642,520
Factor Arrows
215,321,260
Factor Arrows
27,660,630
Factor Arrows
23,830,315
Factor Arrows
5766,063
Factor Arrows
799,697

The prime factorization in exponential form is: 26 x 51 x 791 x 9,6971

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)

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.

245,140,160 = 26 x 51 x 791 x 9,6971
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(245140160) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(245140160) = (7)(2)(2)(2)
Down Arrow
d(245140160) = 56

More numbers for you to try

Take a look at the factors page to see the factors of 245,140,160 and how to find them.

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