Q: What is the prime factorization of the number 432,416?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 13,513
    • or also written as { 2, 2, 2, 2, 2, 13,513 }
  • Written in exponential form: 25 x 13,5131

Why is the prime factorization of 432,416 written as 25 x 13,5131?

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 432,416

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 432,416 by 2

432,416 ÷ 2 = 216,208 - No remainder! 2 is one of the factors!
216,208 ÷ 2 = 108,104 - No remainder! 2 is one of the factors!
108,104 ÷ 2 = 54,052 - No remainder! 2 is one of the factors!
54,052 ÷ 2 = 27,026 - No remainder! 2 is one of the factors!
27,026 ÷ 2 = 13,513 - No remainder! 2 is one of the factors!
13,513 ÷ 2 = 6,756.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
13,513 ÷ 3 = 4,504.3333 - This has a remainder. 3 is not a factor.
13,513 ÷ 5 = 2,702.6 - This has a remainder. 5 is not a factor.
13,513 ÷ 7 = 1,930.4286 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
13,513 ÷ 13,513 = 1 - No remainder! 13,513 is one of the factors!

The orange divisor(s) above are the prime factors of the number 432,416. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 13,513 = 432,416. It can also be written in exponential form as 25 x 13,5131.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 432,416.

432,416
Factor Arrows
2216,208
Factor Arrows
2108,104
Factor Arrows
254,052
Factor Arrows
227,026
Factor Arrows
213,513

More Prime Factorization Examples

432,414432,415432,417432,418
21 x 32 x 24,023151 x 1971 x 439131 x 144,139121 x 71 x 671 x 4611

Try the factor calculator

Explore more about the number 432,416:


Ask a Question