Q: What is the total or count of factors of the number 465,248?

 A: 48

How do I find the total factors of the number 465,248?

Step 1

Find the prime factorization of the number 465,248.

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

Factor Tree
465,248
Factor Arrows
2232,624
Factor Arrows
2116,312
Factor Arrows
258,156
Factor Arrows
229,078
Factor Arrows
214,539
Factor Arrows
72,077
Factor Arrows
3167

The prime factorization in exponential form is: 25 x 71 x 311 x 671

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.

465,248 = 25 x 71 x 311 x 671
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(465248) = (5 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(465248) = (6)(2)(2)(2)
Down Arrow
d(465248) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 465,248 and how to find them.

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