Q: What is the prime factorization of the number 454,144?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 887
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 887 }
  • Written in exponential form: 29 x 8871

Why is the prime factorization of 454,144 written as 29 x 8871?

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 454,144

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 454,144 by 2

454,144 ÷ 2 = 227,072 - No remainder! 2 is one of the factors!
227,072 ÷ 2 = 113,536 - No remainder! 2 is one of the factors!
113,536 ÷ 2 = 56,768 - No remainder! 2 is one of the factors!
56,768 ÷ 2 = 28,384 - No remainder! 2 is one of the factors!
28,384 ÷ 2 = 14,192 - No remainder! 2 is one of the factors!
14,192 ÷ 2 = 7,096 - No remainder! 2 is one of the factors!
7,096 ÷ 2 = 3,548 - No remainder! 2 is one of the factors!
3,548 ÷ 2 = 1,774 - No remainder! 2 is one of the factors!
1,774 ÷ 2 = 887 - No remainder! 2 is one of the factors!
887 ÷ 2 = 443.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
887 ÷ 3 = 295.6667 - This has a remainder. 3 is not a factor.
887 ÷ 5 = 177.4 - This has a remainder. 5 is not a factor.
887 ÷ 7 = 126.7143 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
887 ÷ 887 = 1 - No remainder! 887 is one of the factors!

The orange divisor(s) above are the prime factors of the number 454,144. 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 887 = 454,144. It can also be written in exponential form as 29 x 8871.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 454,144.

454,144
Factor Arrows
2227,072
Factor Arrows
2113,536
Factor Arrows
256,768
Factor Arrows
228,384
Factor Arrows
214,192
Factor Arrows
27,096
Factor Arrows
23,548
Factor Arrows
21,774
Factor Arrows
2887

More Prime Factorization Examples

454,142454,143454,145454,146
21 x 131 x 17,467131 x 151,381151 x 611 x 1,489121 x 31 x 71 x 111 x 9831

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