Q: What is the prime factorization of the number 120,320?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 47
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 47 }
  • Written in exponential form: 29 x 51 x 471

Why is the prime factorization of 120,320 written as 29 x 51 x 471?

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 120,320

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 120,320 by 2

120,320 ÷ 2 = 60,160 - No remainder! 2 is one of the factors!
60,160 ÷ 2 = 30,080 - No remainder! 2 is one of the factors!
30,080 ÷ 2 = 15,040 - No remainder! 2 is one of the factors!
15,040 ÷ 2 = 7,520 - No remainder! 2 is one of the factors!
7,520 ÷ 2 = 3,760 - No remainder! 2 is one of the factors!
3,760 ÷ 2 = 1,880 - No remainder! 2 is one of the factors!
1,880 ÷ 2 = 940 - No remainder! 2 is one of the factors!
940 ÷ 2 = 470 - No remainder! 2 is one of the factors!
470 ÷ 2 = 235 - No remainder! 2 is one of the factors!
235 ÷ 2 = 117.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
235 ÷ 3 = 78.3333 - This has a remainder. 3 is not a factor.
235 ÷ 5 = 47 - No remainder! 5 is one of the factors!
47 ÷ 5 = 9.4 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
47 ÷ 7 = 6.7143 - This has a remainder. 7 is not a factor.
47 ÷ 11 = 4.2727 - This has a remainder. 11 is not a factor.
47 ÷ 13 = 3.6154 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
47 ÷ 47 = 1 - No remainder! 47 is one of the factors!

The orange divisor(s) above are the prime factors of the number 120,320. 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 5 x 47 = 120,320. It can also be written in exponential form as 29 x 51 x 471.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 120,320.

120,320
Factor Arrows
260,160
Factor Arrows
230,080
Factor Arrows
215,040
Factor Arrows
27,520
Factor Arrows
23,760
Factor Arrows
21,880
Factor Arrows
2940
Factor Arrows
2470
Factor Arrows
2235
Factor Arrows
547

More Prime Factorization Examples

120,318120,319120,321120,322
21 x 31 x 111 x 1,8231120,319132 x 291 x 461121 x 60,1611

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