Q: What is the prime factorization of the number 123,904?

The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11 x 11
- or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 11, 11 }
Written in exponential form: 2¹⁰ x 11²

Why is the prime factorization of 123,904 written as 2¹⁰ x 11²?

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 123,904

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 123,904 by 2

123,904 ÷ 2 = 61,952 - No remainder! 2 is one of the factors!
61,952 ÷ 2 = 30,976 - No remainder! 2 is one of the factors!
30,976 ÷ 2 = 15,488 - No remainder! 2 is one of the factors!
15,488 ÷ 2 = 7,744 - No remainder! 2 is one of the factors!
7,744 ÷ 2 = 3,872 - No remainder! 2 is one of the factors!
3,872 ÷ 2 = 1,936 - No remainder! 2 is one of the factors!
1,936 ÷ 2 = 968 - No remainder! 2 is one of the factors!
968 ÷ 2 = 484 - No remainder! 2 is one of the factors!
484 ÷ 2 = 242 - No remainder! 2 is one of the factors!
242 ÷ 2 = 121 - No remainder! 2 is one of the factors!
121 ÷ 2 = 60.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
121 ÷ 3 = 40.3333 - This has a remainder. 3 is not a factor.
121 ÷ 5 = 24.2 - This has a remainder. 5 is not a factor.
121 ÷ 7 = 17.2857 - This has a remainder. 7 is not a factor.
121 ÷ 11 = 11 - No remainder! 11 is one of the factors!
11 ÷ 11 = 1 - No remainder! 11 is one of the factors!

The orange divisor(s) above are the prime factors of the number 123,904. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11 x 11 = 123,904. It can also be written in exponential form as 2¹⁰ x 11².

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 123,904.

	123,904

2		61,952

	2		30,976

		2		15,488

			2		7,744

				2		3,872

					2		1,936

						2		968

							2		484

								2		242

									2		121

										11		11

More Prime Factorization Examples

123,902	123,903	123,905	123,906
2¹ x 41¹ x 1,511¹	3³ x 13¹ x 353¹	5¹ x 24,781¹	2¹ x 3¹ x 107¹ x 193¹

factor calculator

Q: What is the prime factorization of the number 123,904?

Why is the prime factorization of 123,904 written as 2¹⁰ x 11²?

What is prime factorization?

Finding the prime factors of 123,904

If it doesn't make sense yet, let's try it...

Factor Tree

More Prime Factorization Examples

Explore more about the number 123,904:

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Q: What is the prime factorization of the number 123,904?

Why is the prime factorization of 123,904 written as 210 x 112?

What is prime factorization?

Finding the prime factors of 123,904

If it doesn't make sense yet, let's try it...

Factor Tree

More Prime Factorization Examples

Explore more about the number 123,904:

Ask a Question

Why is the prime factorization of 123,904 written as 2¹⁰ x 11²?