Q: What is the prime factorization of the number 777,344?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 6,073
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 6,073 }
  • Written in exponential form: 27 x 6,0731

Why is the prime factorization of 777,344 written as 27 x 6,0731?

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 777,344

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 777,344 by 2

777,344 ÷ 2 = 388,672 - No remainder! 2 is one of the factors!
388,672 ÷ 2 = 194,336 - No remainder! 2 is one of the factors!
194,336 ÷ 2 = 97,168 - No remainder! 2 is one of the factors!
97,168 ÷ 2 = 48,584 - No remainder! 2 is one of the factors!
48,584 ÷ 2 = 24,292 - No remainder! 2 is one of the factors!
24,292 ÷ 2 = 12,146 - No remainder! 2 is one of the factors!
12,146 ÷ 2 = 6,073 - No remainder! 2 is one of the factors!
6,073 ÷ 2 = 3,036.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
6,073 ÷ 3 = 2,024.3333 - This has a remainder. 3 is not a factor.
6,073 ÷ 5 = 1,214.6 - This has a remainder. 5 is not a factor.
6,073 ÷ 7 = 867.5714 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
6,073 ÷ 6,073 = 1 - No remainder! 6,073 is one of the factors!

The orange divisor(s) above are the prime factors of the number 777,344. 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 6,073 = 777,344. It can also be written in exponential form as 27 x 6,0731.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 777,344.

777,344
Factor Arrows
2388,672
Factor Arrows
2194,336
Factor Arrows
297,168
Factor Arrows
248,584
Factor Arrows
224,292
Factor Arrows
212,146
Factor Arrows
26,073

More Prime Factorization Examples

777,342777,343777,345777,346
21 x 31 x 171 x 7,621171 x 111,049131 x 51 x 291 x 1,787121 x 388,6731

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