Q: What is the total or count of factors of the number 46,224?

 A: 40

How do I find the total factors of the number 46,224?

Step 1

Find the prime factorization of the number 46,224.

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

Factor Tree
46,224
Factor Arrows
223,112
Factor Arrows
211,556
Factor Arrows
25,778
Factor Arrows
22,889
Factor Arrows
3963
Factor Arrows
3321
Factor Arrows
3107

The prime factorization in exponential form is: 24 x 33 x 1071

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 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.

46,224 = 24 x 33 x 1071
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(46224) = (4 + 1)(3 + 1)(1 + 1)
Down Arrow
d(46224) = (5)(4)(2)
Down Arrow
d(46224) = 40

More numbers for you to try

Take a look at the factors page to see the factors of 46,224 and how to find them.

Try the factor calculator.

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