Q: What is the total or count of factors of the number 53,758,600?

 A: 192

How do I find the total factors of the number 53,758,600?

Step 1

Find the prime factorization of the number 53,758,600.

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

Factor Tree
53,758,600
Factor Arrows
226,879,300
Factor Arrows
213,439,650
Factor Arrows
26,719,825
Factor Arrows
51,343,965
Factor Arrows
5268,793
Factor Arrows
738,399
Factor Arrows
192,021
Factor Arrows
4347

The prime factorization in exponential form is: 23 x 52 x 71 x 191 x 431 x 471

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.

53,758,600 = 23 x 52 x 71 x 191 x 431 x 471
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(53758600) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(53758600) = (4)(3)(2)(2)(2)(2)
Down Arrow
d(53758600) = 192

More numbers for you to try

Take a look at the factors page to see the factors of 53,758,600 and how to find them.

Try the factor calculator.

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