Q: What is the total or count of factors of the number 72,100,206?

 A: 80

How do I find the total factors of the number 72,100,206?

Step 1

Find the prime factorization of the number 72,100,206.

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

Factor Tree
72,100,206
Factor Arrows
236,050,103
Factor Arrows
312,016,701
Factor Arrows
34,005,567
Factor Arrows
31,335,189
Factor Arrows
3445,063
Factor Arrows
2915,347
Factor Arrows
103149

The prime factorization in exponential form is: 21 x 34 x 291 x 1031 x 1491

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.

72,100,206 = 21 x 34 x 291 x 1031 x 1491
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(72100206) = (1 + 1)(4 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(72100206) = (2)(5)(2)(2)(2)
Down Arrow
d(72100206) = 80

More numbers for you to try

Take a look at the factors page to see the factors of 72,100,206 and how to find them.

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