Q: What is the total or count of factors of the number 503,400?

 A: 48

How do I find the total factors of the number 503,400?

Step 1

Find the prime factorization of the number 503,400.

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

Factor Tree
503,400
Factor Arrows
2251,700
Factor Arrows
2125,850
Factor Arrows
262,925
Factor Arrows
320,975
Factor Arrows
54,195
Factor Arrows
5839

The prime factorization in exponential form is: 23 x 31 x 52 x 8391

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)

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.

503,400 = 23 x 31 x 52 x 8391
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(503400) = (3 + 1)(1 + 1)(2 + 1)(1 + 1)
Down Arrow
d(503400) = (4)(2)(3)(2)
Down Arrow
d(503400) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 503,400 and how to find them.

Try the factor calculator.

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