Q: What is the prime factorization of the number 43,904?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 x 7
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 7, 7, 7 }
  • Written in exponential form: 27 x 73

Why is the prime factorization of 43,904 written as 27 x 73?

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 43,904

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 43,904 by 2

43,904 ÷ 2 = 21,952 - No remainder! 2 is one of the factors!
21,952 ÷ 2 = 10,976 - No remainder! 2 is one of the factors!
10,976 ÷ 2 = 5,488 - No remainder! 2 is one of the factors!
5,488 ÷ 2 = 2,744 - No remainder! 2 is one of the factors!
2,744 ÷ 2 = 1,372 - No remainder! 2 is one of the factors!
1,372 ÷ 2 = 686 - No remainder! 2 is one of the factors!
686 ÷ 2 = 343 - No remainder! 2 is one of the factors!
343 ÷ 2 = 171.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
343 ÷ 3 = 114.3333 - This has a remainder. 3 is not a factor.
343 ÷ 5 = 68.6 - This has a remainder. 5 is not a factor.
343 ÷ 7 = 49 - No remainder! 7 is one of the factors!
49 ÷ 7 = 7 - No remainder! 7 is one of the factors!
7 ÷ 7 = 1 - No remainder! 7 is one of the factors!

The orange divisor(s) above are the prime factors of the number 43,904. 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 7 x 7 x 7 = 43,904. It can also be written in exponential form as 27 x 73.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 43,904.

43,904
Factor Arrows
221,952
Factor Arrows
210,976
Factor Arrows
25,488
Factor Arrows
22,744
Factor Arrows
21,372
Factor Arrows
2686
Factor Arrows
2343
Factor Arrows
749
Factor Arrows
77

More Prime Factorization Examples

43,90243,90343,90543,906
21 x 34 x 2711431 x 1,021131 x 51 x 2,927121 x 291 x 7571

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