Q: What is the total or count of factors of the number 265,320,000?

 A: 420

How do I find the total factors of the number 265,320,000?

Step 1

Find the prime factorization of the number 265,320,000.

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

Factor Tree
265,320,000
Factor Arrows
2132,660,000
Factor Arrows
266,330,000
Factor Arrows
233,165,000
Factor Arrows
216,582,500
Factor Arrows
28,291,250
Factor Arrows
24,145,625
Factor Arrows
31,381,875
Factor Arrows
3460,625
Factor Arrows
592,125
Factor Arrows
518,425
Factor Arrows
53,685
Factor Arrows
5737
Factor Arrows
1167

The prime factorization in exponential form is: 26 x 32 x 54 x 111 x 671

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.

265,320,000 = 26 x 32 x 54 x 111 x 671
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(265320000) = (6 + 1)(2 + 1)(4 + 1)(1 + 1)(1 + 1)
Down Arrow
d(265320000) = (7)(3)(5)(2)(2)
Down Arrow
d(265320000) = 420

More numbers for you to try

Take a look at the factors page to see the factors of 265,320,000 and how to find them.

Try the factor calculator.

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