Q: What is the prime factorization of the number 541,482,127?

Why is the prime factorization of 541,482,127 written as 16,141¹ x 33,547¹?

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 541,482,127

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.

Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 541,482,127 by 2

541,482,127 ÷ 2 = 270,741,063.5 - This has a remainder. Let's try another prime number.
541,482,127 ÷ 3 = 180,494,042.3333 - This has a remainder. Let's try another prime number.
541,482,127 ÷ 5 = 108,296,425.4 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
541,482,127 ÷ 16,141 = 33,547 - No remainder! 16,141 is one of the factors!
33,547 ÷ 16,141 = 2.0784 - There is a remainder. We can't divide by 16141 evenly anymore. Let's try the next prime number
33,547 ÷ 16,183 = 2.073 - This has a remainder. 16,183 is not a factor.
33,547 ÷ 16,187 = 2.0725 - This has a remainder. 16,187 is not a factor.
33,547 ÷ 16,189 = 2.0722 - This has a remainder. 16,189 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
33,547 ÷ 33,547 = 1 - No remainder! 33,547 is one of the factors!

The orange divisor(s) above are the prime factors of the number 541,482,127. If we put all of it together we have the factors 16,141 x 33,547 = 541,482,127. It can also be written in exponential form as 16,141¹ x 33,547¹.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 541,482,127.

	541,482,127
16,141		33,547

More Prime Factorization Examples

Try the factor calculator