Q: What is the prime factorization of the number 47,872?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11 x 17
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 11, 17 }
  • Written in exponential form: 28 x 111 x 171

Why is the prime factorization of 47,872 written as 28 x 111 x 171?

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 47,872

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 47,872 by 2

47,872 ÷ 2 = 23,936 - No remainder! 2 is one of the factors!
23,936 ÷ 2 = 11,968 - No remainder! 2 is one of the factors!
11,968 ÷ 2 = 5,984 - No remainder! 2 is one of the factors!
5,984 ÷ 2 = 2,992 - No remainder! 2 is one of the factors!
2,992 ÷ 2 = 1,496 - No remainder! 2 is one of the factors!
1,496 ÷ 2 = 748 - No remainder! 2 is one of the factors!
748 ÷ 2 = 374 - No remainder! 2 is one of the factors!
374 ÷ 2 = 187 - No remainder! 2 is one of the factors!
187 ÷ 2 = 93.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
187 ÷ 3 = 62.3333 - This has a remainder. 3 is not a factor.
187 ÷ 5 = 37.4 - This has a remainder. 5 is not a factor.
187 ÷ 7 = 26.7143 - This has a remainder. 7 is not a factor.
187 ÷ 11 = 17 - No remainder! 11 is one of the factors!
17 ÷ 11 = 1.5455 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
17 ÷ 13 = 1.3077 - This has a remainder. 13 is not a factor.
17 ÷ 17 = 1 - No remainder! 17 is one of the factors!

The orange divisor(s) above are the prime factors of the number 47,872. 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 11 x 17 = 47,872. It can also be written in exponential form as 28 x 111 x 171.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 47,872.

47,872
Factor Arrows
223,936
Factor Arrows
211,968
Factor Arrows
25,984
Factor Arrows
22,992
Factor Arrows
21,496
Factor Arrows
2748
Factor Arrows
2374
Factor Arrows
2187
Factor Arrows
1117

More Prime Factorization Examples

47,87047,87147,87347,874
21 x 51 x 4,787135 x 197172 x 977121 x 31 x 791 x 1011

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