Q: What is the prime factorization of the number 301,248?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 523
    • or also written as { 2, 2, 2, 2, 2, 2, 3, 3, 523 }
  • Written in exponential form: 26 x 32 x 5231

Why is the prime factorization of 301,248 written as 26 x 32 x 5231?

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 301,248

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 301,248 by 2

301,248 ÷ 2 = 150,624 - No remainder! 2 is one of the factors!
150,624 ÷ 2 = 75,312 - No remainder! 2 is one of the factors!
75,312 ÷ 2 = 37,656 - No remainder! 2 is one of the factors!
37,656 ÷ 2 = 18,828 - No remainder! 2 is one of the factors!
18,828 ÷ 2 = 9,414 - No remainder! 2 is one of the factors!
9,414 ÷ 2 = 4,707 - No remainder! 2 is one of the factors!
4,707 ÷ 2 = 2,353.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
4,707 ÷ 3 = 1,569 - No remainder! 3 is one of the factors!
1,569 ÷ 3 = 523 - No remainder! 3 is one of the factors!
523 ÷ 3 = 174.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
523 ÷ 5 = 104.6 - This has a remainder. 5 is not a factor.
523 ÷ 7 = 74.7143 - This has a remainder. 7 is not a factor.
523 ÷ 11 = 47.5455 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
523 ÷ 523 = 1 - No remainder! 523 is one of the factors!

The orange divisor(s) above are the prime factors of the number 301,248. 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 3 x 523 = 301,248. It can also be written in exponential form as 26 x 32 x 5231.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 301,248.

301,248
Factor Arrows
2150,624
Factor Arrows
275,312
Factor Arrows
237,656
Factor Arrows
218,828
Factor Arrows
29,414
Factor Arrows
24,707
Factor Arrows
31,569
Factor Arrows
3523

More Prime Factorization Examples

301,246301,247301,249301,250
21 x 111 x 13,6931301,2471131 x 23,173121 x 54 x 2411

Try the factor calculator

Explore more about the number 301,248:


Ask a Question