Q: What is the prime factorization of the number 544,653?

 A:
  • The prime factors are: 3 x 3 x 73 x 829
    • or also written as { 3, 3, 73, 829 }
  • Written in exponential form: 32 x 731 x 8291

Why is the prime factorization of 544,653 written as 32 x 731 x 8291?

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 544,653

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 544,653 by 2

544,653 ÷ 2 = 272,326.5 - This has a remainder. Let's try another prime number.
544,653 ÷ 3 = 181,551 - No remainder! 3 is one of the factors!
181,551 ÷ 3 = 60,517 - No remainder! 3 is one of the factors!
60,517 ÷ 3 = 20,172.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
60,517 ÷ 5 = 12,103.4 - This has a remainder. 5 is not a factor.
60,517 ÷ 7 = 8,645.2857 - This has a remainder. 7 is not a factor.
60,517 ÷ 11 = 5,501.5455 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
60,517 ÷ 73 = 829 - No remainder! 73 is one of the factors!
829 ÷ 73 = 11.3562 - There is a remainder. We can't divide by 73 evenly anymore. Let's try the next prime number
829 ÷ 79 = 10.4937 - This has a remainder. 79 is not a factor.
829 ÷ 83 = 9.988 - This has a remainder. 83 is not a factor.
829 ÷ 89 = 9.3146 - This has a remainder. 89 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
829 ÷ 829 = 1 - No remainder! 829 is one of the factors!

The orange divisor(s) above are the prime factors of the number 544,653. If we put all of it together we have the factors 3 x 3 x 73 x 829 = 544,653. It can also be written in exponential form as 32 x 731 x 8291.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 544,653.

544,653
Factor Arrows
3181,551
Factor Arrows
360,517
Factor Arrows
73829

More Prime Factorization Examples

544,651544,652544,654544,655
544,651122 x 136,163121 x 111 x 191 x 1,303151 x 971 x 1,1231

Try the factor calculator

Explore more about the number 544,653:


Ask a Question