Q: What is the total or count of factors of the number 661,248?

 A: 108

How do I find the total factors of the number 661,248?

Step 1

Find the prime factorization of the number 661,248.

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

Factor Tree
661,248
Factor Arrows
2330,624
Factor Arrows
2165,312
Factor Arrows
282,656
Factor Arrows
241,328
Factor Arrows
220,664
Factor Arrows
210,332
Factor Arrows
25,166
Factor Arrows
22,583
Factor Arrows
3861
Factor Arrows
3287
Factor Arrows
741

The prime factorization in exponential form is: 28 x 32 x 71 x 411

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.

661,248 = 28 x 32 x 71 x 411
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(661248) = (8 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(661248) = (9)(3)(2)(2)
Down Arrow
d(661248) = 108

More numbers for you to try

Take a look at the factors page to see the factors of 661,248 and how to find them.

Try the factor calculator.

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