Q: What is the total or count of factors of the number 52,013,500?

 A: 144

How do I find the total factors of the number 52,013,500?

Step 1

Find the prime factorization of the number 52,013,500.

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

Factor Tree
52,013,500
Factor Arrows
226,006,750
Factor Arrows
213,003,375
Factor Arrows
52,600,675
Factor Arrows
5520,135
Factor Arrows
5104,027
Factor Arrows
714,861
Factor Arrows
72,123
Factor Arrows
11193

The prime factorization in exponential form is: 22 x 53 x 72 x 111 x 1931

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.

52,013,500 = 22 x 53 x 72 x 111 x 1931
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(52013500) = (2 + 1)(3 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(52013500) = (3)(4)(3)(2)(2)
Down Arrow
d(52013500) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 52,013,500 and how to find them.

Try the factor calculator.

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