Q: What is the prime factorization of the number 911,936?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 14,249
    • or also written as { 2, 2, 2, 2, 2, 2, 14,249 }
  • Written in exponential form: 26 x 14,2491

Why is the prime factorization of 911,936 written as 26 x 14,2491?

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 911,936

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 911,936 by 2

911,936 ÷ 2 = 455,968 - No remainder! 2 is one of the factors!
455,968 ÷ 2 = 227,984 - No remainder! 2 is one of the factors!
227,984 ÷ 2 = 113,992 - No remainder! 2 is one of the factors!
113,992 ÷ 2 = 56,996 - No remainder! 2 is one of the factors!
56,996 ÷ 2 = 28,498 - No remainder! 2 is one of the factors!
28,498 ÷ 2 = 14,249 - No remainder! 2 is one of the factors!
14,249 ÷ 2 = 7,124.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
14,249 ÷ 3 = 4,749.6667 - This has a remainder. 3 is not a factor.
14,249 ÷ 5 = 2,849.8 - This has a remainder. 5 is not a factor.
14,249 ÷ 7 = 2,035.5714 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
14,249 ÷ 14,249 = 1 - No remainder! 14,249 is one of the factors!

The orange divisor(s) above are the prime factors of the number 911,936. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 14,249 = 911,936. It can also be written in exponential form as 26 x 14,2491.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 911,936.

911,936
Factor Arrows
2455,968
Factor Arrows
2227,984
Factor Arrows
2113,992
Factor Arrows
256,996
Factor Arrows
228,498
Factor Arrows
214,249

More Prime Factorization Examples

911,934911,935911,937911,938
21 x 32 x 291 x 1,747151 x 182,387131 x 131 x 671 x 349121 x 455,9691

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