Q: What is the prime factorization of the number 11,345,920?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 277
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 277 }
  • Written in exponential form: 213 x 51 x 2771

Why is the prime factorization of 11,345,920 written as 213 x 51 x 2771?

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 11,345,920

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 11,345,920 by 2

11,345,920 ÷ 2 = 5,672,960 - No remainder! 2 is one of the factors!
5,672,960 ÷ 2 = 2,836,480 - No remainder! 2 is one of the factors!
2,836,480 ÷ 2 = 1,418,240 - No remainder! 2 is one of the factors!
1,418,240 ÷ 2 = 709,120 - No remainder! 2 is one of the factors!
709,120 ÷ 2 = 354,560 - No remainder! 2 is one of the factors!
354,560 ÷ 2 = 177,280 - No remainder! 2 is one of the factors!
177,280 ÷ 2 = 88,640 - No remainder! 2 is one of the factors!
88,640 ÷ 2 = 44,320 - No remainder! 2 is one of the factors!
44,320 ÷ 2 = 22,160 - No remainder! 2 is one of the factors!
22,160 ÷ 2 = 11,080 - No remainder! 2 is one of the factors!
11,080 ÷ 2 = 5,540 - No remainder! 2 is one of the factors!
5,540 ÷ 2 = 2,770 - No remainder! 2 is one of the factors!
2,770 ÷ 2 = 1,385 - No remainder! 2 is one of the factors!
1,385 ÷ 2 = 692.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
1,385 ÷ 3 = 461.6667 - This has a remainder. 3 is not a factor.
1,385 ÷ 5 = 277 - No remainder! 5 is one of the factors!
277 ÷ 5 = 55.4 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
277 ÷ 7 = 39.5714 - This has a remainder. 7 is not a factor.
277 ÷ 11 = 25.1818 - This has a remainder. 11 is not a factor.
277 ÷ 13 = 21.3077 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
277 ÷ 277 = 1 - No remainder! 277 is one of the factors!

The orange divisor(s) above are the prime factors of the number 11,345,920. 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 2 x 2 x 2 x 5 x 277 = 11,345,920. It can also be written in exponential form as 213 x 51 x 2771.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 11,345,920.

11,345,920
Factor Arrows
25,672,960
Factor Arrows
22,836,480
Factor Arrows
21,418,240
Factor Arrows
2709,120
Factor Arrows
2354,560
Factor Arrows
2177,280
Factor Arrows
288,640
Factor Arrows
244,320
Factor Arrows
222,160
Factor Arrows
211,080
Factor Arrows
25,540
Factor Arrows
22,770
Factor Arrows
21,385
Factor Arrows
5277

More Prime Factorization Examples

11,345,91811,345,91911,345,92111,345,922
21 x 5,672,959131 x 131 x 171 x 1091 x 157111,345,921121 x 32 x 71 x 531 x 1,6991

Try the factor calculator

Explore more about the number 11,345,920:


Ask a Question