Q: What is the prime factorization of the number 333,532,647?

 A:
  • The prime factors are: 3 x 3 x 3 x 3 x 7 x 588,241
    • or also written as { 3, 3, 3, 3, 7, 588,241 }
  • Written in exponential form: 34 x 71 x 588,2411

Why is the prime factorization of 333,532,647 written as 34 x 71 x 588,2411?

What is prime factorization?

Prime factorization or prime factor decomposition is the process of finding which prime numbers can be multiplied together to make the original number.

Finding the prime factors of 333,532,647

To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.

If it doesn't make sense yet, let's try it...

Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 333,532,647 by 2

333,532,647 ÷ 2 = 166,766,323.5 - This has a remainder. Let's try another prime number.
333,532,647 ÷ 3 = 111,177,549 - No remainder! 3 is one of the factors!
111,177,549 ÷ 3 = 37,059,183 - No remainder! 3 is one of the factors!
37,059,183 ÷ 3 = 12,353,061 - No remainder! 3 is one of the factors!
12,353,061 ÷ 3 = 4,117,687 - No remainder! 3 is one of the factors!
4,117,687 ÷ 3 = 1,372,562.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
4,117,687 ÷ 5 = 823,537.4 - This has a remainder. 5 is not a factor.
4,117,687 ÷ 7 = 588,241 - No remainder! 7 is one of the factors!
588,241 ÷ 7 = 84,034.4286 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
588,241 ÷ 11 = 53,476.4545 - This has a remainder. 11 is not a factor.
588,241 ÷ 13 = 45,249.3077 - This has a remainder. 13 is not a factor.
588,241 ÷ 17 = 34,602.4118 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
588,241 ÷ 588,241 = 1 - No remainder! 588,241 is one of the factors!

The orange divisor(s) above are the prime factors of the number 333,532,647. If we put all of it together we have the factors 3 x 3 x 3 x 3 x 7 x 588,241 = 333,532,647. It can also be written in exponential form as 34 x 71 x 588,2411.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 333,532,647.

333,532,647
Factor Arrows
3111,177,549
Factor Arrows
337,059,183
Factor Arrows
312,353,061
Factor Arrows
34,117,687
Factor Arrows
7588,241

More Prime Factorization Examples

333,532,645333,532,646333,532,648333,532,649
51 x 5,7911 x 11,519121 x 9371 x 177,979123 x 4,3371 x 9,61312,5311 x 131,7791

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