Q: What is the total or count of factors of the number 625,772,040?

 A: 128

How do I find the total factors of the number 625,772,040?

Step 1

Find the prime factorization of the number 625,772,040.

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

Factor Tree
625,772,040
Factor Arrows
2312,886,020
Factor Arrows
2156,443,010
Factor Arrows
278,221,505
Factor Arrows
326,073,835
Factor Arrows
55,214,767
Factor Arrows
17306,751
Factor Arrows
2313,337

The prime factorization in exponential form is: 23 x 31 x 51 x 171 x 231 x 13,3371

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)(f + 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.

625,772,040 = 23 x 31 x 51 x 171 x 231 x 13,3371
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(625772040) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(625772040) = (4)(2)(2)(2)(2)(2)
Down Arrow
d(625772040) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 625,772,040 and how to find them.

Try the factor calculator.

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