Q: What is the total or count of factors of the number 53,416,125?

 A: 192

How do I find the total factors of the number 53,416,125?

Step 1

Find the prime factorization of the number 53,416,125.

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

Factor Tree
53,416,125
Factor Arrows
317,805,375
Factor Arrows
35,935,125
Factor Arrows
31,978,375
Factor Arrows
5395,675
Factor Arrows
579,135
Factor Arrows
515,827
Factor Arrows
72,261
Factor Arrows
7323
Factor Arrows
1719

The prime factorization in exponential form is: 33 x 53 x 72 x 171 x 191

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.

53,416,125 = 33 x 53 x 72 x 171 x 191
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(53416125) = (3 + 1)(3 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(53416125) = (4)(4)(3)(2)(2)
Down Arrow
d(53416125) = 192

More numbers for you to try

Take a look at the factors page to see the factors of 53,416,125 and how to find them.

Try the factor calculator.

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