Q: What is the prime factorization of the number 153,504?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 41
    • or also written as { 2, 2, 2, 2, 2, 3, 3, 13, 41 }
  • Written in exponential form: 25 x 32 x 131 x 411

Why is the prime factorization of 153,504 written as 25 x 32 x 131 x 411?

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 153,504

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 153,504 by 2

153,504 ÷ 2 = 76,752 - No remainder! 2 is one of the factors!
76,752 ÷ 2 = 38,376 - No remainder! 2 is one of the factors!
38,376 ÷ 2 = 19,188 - No remainder! 2 is one of the factors!
19,188 ÷ 2 = 9,594 - No remainder! 2 is one of the factors!
9,594 ÷ 2 = 4,797 - No remainder! 2 is one of the factors!
4,797 ÷ 2 = 2,398.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
4,797 ÷ 3 = 1,599 - No remainder! 3 is one of the factors!
1,599 ÷ 3 = 533 - No remainder! 3 is one of the factors!
533 ÷ 3 = 177.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
533 ÷ 5 = 106.6 - This has a remainder. 5 is not a factor.
533 ÷ 7 = 76.1429 - This has a remainder. 7 is not a factor.
533 ÷ 11 = 48.4545 - This has a remainder. 11 is not a factor.
533 ÷ 13 = 41 - No remainder! 13 is one of the factors!
41 ÷ 13 = 3.1538 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
41 ÷ 17 = 2.4118 - This has a remainder. 17 is not a factor.
41 ÷ 19 = 2.1579 - This has a remainder. 19 is not a factor.
41 ÷ 23 = 1.7826 - This has a remainder. 23 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
41 ÷ 41 = 1 - No remainder! 41 is one of the factors!

The orange divisor(s) above are the prime factors of the number 153,504. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 41 = 153,504. It can also be written in exponential form as 25 x 32 x 131 x 411.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 153,504.

153,504
Factor Arrows
276,752
Factor Arrows
238,376
Factor Arrows
219,188
Factor Arrows
29,594
Factor Arrows
24,797
Factor Arrows
31,599
Factor Arrows
3533
Factor Arrows
1341

More Prime Factorization Examples

153,502153,503153,505153,506
21 x 231 x 471 x 71171 x 21,929151 x 111 x 2,791121 x 76,7531

Try the factor calculator

Explore more about the number 153,504:


Ask a Question