Q: What is the total or count of factors of the number 9,227,460?

 A: 144

How do I find the total factors of the number 9,227,460?

Step 1

Find the prime factorization of the number 9,227,460.

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

Factor Tree
9,227,460
Factor Arrows
24,613,730
Factor Arrows
22,306,865
Factor Arrows
3768,955
Factor Arrows
5153,791
Factor Arrows
1113,981
Factor Arrows
111,271
Factor Arrows
3141

The prime factorization in exponential form is: 22 x 31 x 51 x 112 x 311 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)(e + 1)(f + 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.

9,227,460 = 22 x 31 x 51 x 112 x 311 x 411
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(9227460) = (2 + 1)(1 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(9227460) = (3)(2)(2)(3)(2)(2)
Down Arrow
d(9227460) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 9,227,460 and how to find them.

Try the factor calculator.

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