Q: What is the total or count of factors of the number 72,027,360?

 A: 96

How do I find the total factors of the number 72,027,360?

Step 1

Find the prime factorization of the number 72,027,360.

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

Factor Tree
72,027,360
Factor Arrows
236,013,680
Factor Arrows
218,006,840
Factor Arrows
29,003,420
Factor Arrows
24,501,710
Factor Arrows
22,250,855
Factor Arrows
3750,285
Factor Arrows
3250,095
Factor Arrows
383,365
Factor Arrows
516,673

The prime factorization in exponential form is: 25 x 33 x 51 x 16,6731

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.

72,027,360 = 25 x 33 x 51 x 16,6731
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(72027360) = (5 + 1)(3 + 1)(1 + 1)(1 + 1)
Down Arrow
d(72027360) = (6)(4)(2)(2)
Down Arrow
d(72027360) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 72,027,360 and how to find them.

Try the factor calculator.

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