Q: What is the total or count of factors of the number 2,689,830?

 A: 144

How do I find the total factors of the number 2,689,830?

Step 1

Find the prime factorization of the number 2,689,830.

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

Factor Tree
2,689,830
Factor Arrows
21,344,915
Factor Arrows
3448,305
Factor Arrows
3149,435
Factor Arrows
529,887
Factor Arrows
112,717
Factor Arrows
11247
Factor Arrows
1319

The prime factorization in exponential form is: 21 x 32 x 51 x 112 x 131 x 191

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.

2,689,830 = 21 x 32 x 51 x 112 x 131 x 191
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(2689830) = (1 + 1)(2 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(2689830) = (2)(3)(2)(3)(2)(2)
Down Arrow
d(2689830) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 2,689,830 and how to find them.

Try the factor calculator.

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