Q: What is the prime factorization of the number 551,616?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 13 x 17
    • or also written as { 2, 2, 2, 2, 2, 2, 3, 13, 13, 17 }
  • Written in exponential form: 26 x 31 x 132 x 171

Why is the prime factorization of 551,616 written as 26 x 31 x 132 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 551,616

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 551,616 by 2

551,616 ÷ 2 = 275,808 - No remainder! 2 is one of the factors!
275,808 ÷ 2 = 137,904 - No remainder! 2 is one of the factors!
137,904 ÷ 2 = 68,952 - No remainder! 2 is one of the factors!
68,952 ÷ 2 = 34,476 - No remainder! 2 is one of the factors!
34,476 ÷ 2 = 17,238 - No remainder! 2 is one of the factors!
17,238 ÷ 2 = 8,619 - No remainder! 2 is one of the factors!
8,619 ÷ 2 = 4,309.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
8,619 ÷ 3 = 2,873 - No remainder! 3 is one of the factors!
2,873 ÷ 3 = 957.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
2,873 ÷ 5 = 574.6 - This has a remainder. 5 is not a factor.
2,873 ÷ 7 = 410.4286 - This has a remainder. 7 is not a factor.
2,873 ÷ 11 = 261.1818 - This has a remainder. 11 is not a factor.
2,873 ÷ 13 = 221 - No remainder! 13 is one of the factors!
221 ÷ 13 = 17 - No remainder! 13 is one of the factors!
17 ÷ 13 = 1.3077 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
17 ÷ 17 = 1 - No remainder! 17 is one of the factors!

The orange divisor(s) above are the prime factors of the number 551,616. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 13 x 17 = 551,616. It can also be written in exponential form as 26 x 31 x 132 x 171.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 551,616.

551,616
Factor Arrows
2275,808
Factor Arrows
2137,904
Factor Arrows
268,952
Factor Arrows
234,476
Factor Arrows
217,238
Factor Arrows
28,619
Factor Arrows
32,873
Factor Arrows
13221
Factor Arrows
1317

More Prime Factorization Examples

551,614551,615551,617551,618
21 x 71 x 312 x 41151 x 110,3231111 x 50,147121 x 831 x 3,3231

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