Q: What is the prime factorization of the number 245,888?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 17 x 113
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 17, 113 }
  • Written in exponential form: 27 x 171 x 1131

Why is the prime factorization of 245,888 written as 27 x 171 x 1131?

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 245,888

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 245,888 by 2

245,888 ÷ 2 = 122,944 - No remainder! 2 is one of the factors!
122,944 ÷ 2 = 61,472 - No remainder! 2 is one of the factors!
61,472 ÷ 2 = 30,736 - No remainder! 2 is one of the factors!
30,736 ÷ 2 = 15,368 - No remainder! 2 is one of the factors!
15,368 ÷ 2 = 7,684 - No remainder! 2 is one of the factors!
7,684 ÷ 2 = 3,842 - No remainder! 2 is one of the factors!
3,842 ÷ 2 = 1,921 - No remainder! 2 is one of the factors!
1,921 ÷ 2 = 960.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
1,921 ÷ 3 = 640.3333 - This has a remainder. 3 is not a factor.
1,921 ÷ 5 = 384.2 - This has a remainder. 5 is not a factor.
1,921 ÷ 7 = 274.4286 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
1,921 ÷ 17 = 113 - No remainder! 17 is one of the factors!
113 ÷ 17 = 6.6471 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
113 ÷ 19 = 5.9474 - This has a remainder. 19 is not a factor.
113 ÷ 23 = 4.913 - This has a remainder. 23 is not a factor.
113 ÷ 29 = 3.8966 - This has a remainder. 29 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
113 ÷ 113 = 1 - No remainder! 113 is one of the factors!

The orange divisor(s) above are the prime factors of the number 245,888. 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 17 x 113 = 245,888. It can also be written in exponential form as 27 x 171 x 1131.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 245,888.

245,888
Factor Arrows
2122,944
Factor Arrows
261,472
Factor Arrows
230,736
Factor Arrows
215,368
Factor Arrows
27,684
Factor Arrows
23,842
Factor Arrows
21,921
Factor Arrows
17113

More Prime Factorization Examples

245,886245,887245,889245,890
21 x 31 x 1071 x 38311311 x 1,877133 x 71 x 1,301121 x 51 x 671 x 3671

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