Q: What is the total or count of factors of the number 17,533,632?

 A: 112

How do I find the total factors of the number 17,533,632?

Step 1

Find the prime factorization of the number 17,533,632.

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

Factor Tree
17,533,632
Factor Arrows
28,766,816
Factor Arrows
24,383,408
Factor Arrows
22,191,704
Factor Arrows
21,095,852
Factor Arrows
2547,926
Factor Arrows
2273,963
Factor Arrows
391,321
Factor Arrows
293,149
Factor Arrows
4767

The prime factorization in exponential form is: 26 x 31 x 291 x 471 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)(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.

17,533,632 = 26 x 31 x 291 x 471 x 671
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(17533632) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(17533632) = (7)(2)(2)(2)(2)
Down Arrow
d(17533632) = 112

More numbers for you to try

Take a look at the factors page to see the factors of 17,533,632 and how to find them.

Try the factor calculator.

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