Q: What is the total or count of factors of the number 665,533,152?

 A: 192

How do I find the total factors of the number 665,533,152?

Step 1

Find the prime factorization of the number 665,533,152.

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

Factor Tree
665,533,152
Factor Arrows
2332,766,576
Factor Arrows
2166,383,288
Factor Arrows
283,191,644
Factor Arrows
241,595,822
Factor Arrows
220,797,911
Factor Arrows
36,932,637
Factor Arrows
32,310,879
Factor Arrows
3770,293
Factor Arrows
2333,491
Factor Arrows
107313

The prime factorization in exponential form is: 25 x 33 x 231 x 1071 x 3131

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.

665,533,152 = 25 x 33 x 231 x 1071 x 3131
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(665533152) = (5 + 1)(3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(665533152) = (6)(4)(2)(2)(2)
Down Arrow
d(665533152) = 192

More numbers for you to try

Take a look at the factors page to see the factors of 665,533,152 and how to find them.

Try the factor calculator.

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