Q: What is the total or count of factors of the number 4,165,140?

 A: 96

How do I find the total factors of the number 4,165,140?

Step 1

Find the prime factorization of the number 4,165,140.

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

Factor Tree
4,165,140
Factor Arrows
22,082,570
Factor Arrows
21,041,285
Factor Arrows
3347,095
Factor Arrows
569,419
Factor Arrows
79,917
Factor Arrows
47211

The prime factorization in exponential form is: 22 x 31 x 51 x 71 x 471 x 2111

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.

4,165,140 = 22 x 31 x 51 x 71 x 471 x 2111
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(4165140) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(4165140) = (3)(2)(2)(2)(2)(2)
Down Arrow
d(4165140) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 4,165,140 and how to find them.

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