Q: What is the total or count of factors of the number 211,322,540?

 A: 96

How do I find the total factors of the number 211,322,540?

Step 1

Find the prime factorization of the number 211,322,540.

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

Factor Tree
211,322,540
Factor Arrows
2105,661,270
Factor Arrows
252,830,635
Factor Arrows
510,566,127
Factor Arrows
11960,557
Factor Arrows
1373,889
Factor Arrows
371,997

The prime factorization in exponential form is: 22 x 51 x 111 x 131 x 371 x 1,9971

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.

211,322,540 = 22 x 51 x 111 x 131 x 371 x 1,9971
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(211322540) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(211322540) = (3)(2)(2)(2)(2)(2)
Down Arrow
d(211322540) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 211,322,540 and how to find them.

Try the factor calculator.

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