Q: What is the prime factorization of the number 2,783,232?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 151
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 151 }
  • Written in exponential form: 211 x 32 x 1511

Why is the prime factorization of 2,783,232 written as 211 x 32 x 1511?

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 2,783,232

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 2,783,232 by 2

2,783,232 ÷ 2 = 1,391,616 - No remainder! 2 is one of the factors!
1,391,616 ÷ 2 = 695,808 - No remainder! 2 is one of the factors!
695,808 ÷ 2 = 347,904 - No remainder! 2 is one of the factors!
347,904 ÷ 2 = 173,952 - No remainder! 2 is one of the factors!
173,952 ÷ 2 = 86,976 - No remainder! 2 is one of the factors!
86,976 ÷ 2 = 43,488 - No remainder! 2 is one of the factors!
43,488 ÷ 2 = 21,744 - No remainder! 2 is one of the factors!
21,744 ÷ 2 = 10,872 - No remainder! 2 is one of the factors!
10,872 ÷ 2 = 5,436 - No remainder! 2 is one of the factors!
5,436 ÷ 2 = 2,718 - No remainder! 2 is one of the factors!
2,718 ÷ 2 = 1,359 - No remainder! 2 is one of the factors!
1,359 ÷ 2 = 679.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
1,359 ÷ 3 = 453 - No remainder! 3 is one of the factors!
453 ÷ 3 = 151 - No remainder! 3 is one of the factors!
151 ÷ 3 = 50.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
151 ÷ 5 = 30.2 - This has a remainder. 5 is not a factor.
151 ÷ 7 = 21.5714 - This has a remainder. 7 is not a factor.
151 ÷ 11 = 13.7273 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
151 ÷ 151 = 1 - No remainder! 151 is one of the factors!

The orange divisor(s) above are the prime factors of the number 2,783,232. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 151 = 2,783,232. It can also be written in exponential form as 211 x 32 x 1511.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 2,783,232.

2,783,232
Factor Arrows
21,391,616
Factor Arrows
2695,808
Factor Arrows
2347,904
Factor Arrows
2173,952
Factor Arrows
286,976
Factor Arrows
243,488
Factor Arrows
221,744
Factor Arrows
210,872
Factor Arrows
25,436
Factor Arrows
22,718
Factor Arrows
21,359
Factor Arrows
3453
Factor Arrows
3151

More Prime Factorization Examples

2,783,2302,783,2312,783,2332,783,234
21 x 51 x 231 x 12,1011111 x 4211 x 60119471 x 2,939121 x 191 x 73,2431

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