Q: What is the total or count of factors of the number 27,001,440?

 A: 144

How do I find the total factors of the number 27,001,440?

Step 1

Find the prime factorization of the number 27,001,440.

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

Factor Tree
27,001,440
Factor Arrows
213,500,720
Factor Arrows
26,750,360
Factor Arrows
23,375,180
Factor Arrows
21,687,590
Factor Arrows
2843,795
Factor Arrows
3281,265
Factor Arrows
393,755
Factor Arrows
518,751
Factor Arrows
171,103

The prime factorization in exponential form is: 25 x 32 x 51 x 171 x 1,1031

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.

27,001,440 = 25 x 32 x 51 x 171 x 1,1031
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(27001440) = (5 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(27001440) = (6)(3)(2)(2)(2)
Down Arrow
d(27001440) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 27,001,440 and how to find them.

Try the factor calculator.

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