Q: What is the total or count of factors of the number 35,533,410?

 A: 128

How do I find the total factors of the number 35,533,410?

Step 1

Find the prime factorization of the number 35,533,410.

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

Factor Tree
35,533,410
Factor Arrows
217,766,705
Factor Arrows
35,922,235
Factor Arrows
51,184,447
Factor Arrows
11107,677
Factor Arrows
293,713
Factor Arrows
4779

The prime factorization in exponential form is: 21 x 31 x 51 x 111 x 291 x 471 x 791

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)(f + 1)(g + 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.

35,533,410 = 21 x 31 x 51 x 111 x 291 x 471 x 791
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)(g + 1)
Down Arrow
d(35533410) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(35533410) = (2)(2)(2)(2)(2)(2)(2)
Down Arrow
d(35533410) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 35,533,410 and how to find them.

Try the factor calculator.

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