Q: What is the prime factorization of the number 552,240?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 3 x 3 x 5 x 13 x 59
    • or also written as { 2, 2, 2, 2, 3, 3, 5, 13, 59 }
  • Written in exponential form: 24 x 32 x 51 x 131 x 591

Why is the prime factorization of 552,240 written as 24 x 32 x 51 x 131 x 591?

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 552,240

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 552,240 by 2

552,240 ÷ 2 = 276,120 - No remainder! 2 is one of the factors!
276,120 ÷ 2 = 138,060 - No remainder! 2 is one of the factors!
138,060 ÷ 2 = 69,030 - No remainder! 2 is one of the factors!
69,030 ÷ 2 = 34,515 - No remainder! 2 is one of the factors!
34,515 ÷ 2 = 17,257.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
34,515 ÷ 3 = 11,505 - No remainder! 3 is one of the factors!
11,505 ÷ 3 = 3,835 - No remainder! 3 is one of the factors!
3,835 ÷ 3 = 1,278.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
3,835 ÷ 5 = 767 - No remainder! 5 is one of the factors!
767 ÷ 5 = 153.4 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
767 ÷ 7 = 109.5714 - This has a remainder. 7 is not a factor.
767 ÷ 11 = 69.7273 - This has a remainder. 11 is not a factor.
767 ÷ 13 = 59 - No remainder! 13 is one of the factors!
59 ÷ 13 = 4.5385 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
59 ÷ 17 = 3.4706 - This has a remainder. 17 is not a factor.
59 ÷ 19 = 3.1053 - This has a remainder. 19 is not a factor.
59 ÷ 23 = 2.5652 - This has a remainder. 23 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
59 ÷ 59 = 1 - No remainder! 59 is one of the factors!

The orange divisor(s) above are the prime factors of the number 552,240. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 3 x 3 x 5 x 13 x 59 = 552,240. It can also be written in exponential form as 24 x 32 x 51 x 131 x 591.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 552,240.

552,240
Factor Arrows
2276,120
Factor Arrows
2138,060
Factor Arrows
269,030
Factor Arrows
234,515
Factor Arrows
311,505
Factor Arrows
33,835
Factor Arrows
5767
Factor Arrows
1359

More Prime Factorization Examples

552,238552,239552,241552,242
21 x 711 x 3,8891552,2391552,241121 x 4191 x 6591

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