Q: What is the prime factorization of the number 13,882,880?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 11 x 17 x 29
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 11, 17, 29 }
  • Written in exponential form: 29 x 51 x 111 x 171 x 291

Why is the prime factorization of 13,882,880 written as 29 x 51 x 111 x 171 x 291?

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 13,882,880

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 13,882,880 by 2

13,882,880 ÷ 2 = 6,941,440 - No remainder! 2 is one of the factors!
6,941,440 ÷ 2 = 3,470,720 - No remainder! 2 is one of the factors!
3,470,720 ÷ 2 = 1,735,360 - No remainder! 2 is one of the factors!
1,735,360 ÷ 2 = 867,680 - No remainder! 2 is one of the factors!
867,680 ÷ 2 = 433,840 - No remainder! 2 is one of the factors!
433,840 ÷ 2 = 216,920 - No remainder! 2 is one of the factors!
216,920 ÷ 2 = 108,460 - No remainder! 2 is one of the factors!
108,460 ÷ 2 = 54,230 - No remainder! 2 is one of the factors!
54,230 ÷ 2 = 27,115 - No remainder! 2 is one of the factors!
27,115 ÷ 2 = 13,557.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
27,115 ÷ 3 = 9,038.3333 - This has a remainder. 3 is not a factor.
27,115 ÷ 5 = 5,423 - No remainder! 5 is one of the factors!
5,423 ÷ 5 = 1,084.6 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
5,423 ÷ 7 = 774.7143 - This has a remainder. 7 is not a factor.
5,423 ÷ 11 = 493 - No remainder! 11 is one of the factors!
493 ÷ 11 = 44.8182 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
493 ÷ 13 = 37.9231 - This has a remainder. 13 is not a factor.
493 ÷ 17 = 29 - No remainder! 17 is one of the factors!
29 ÷ 17 = 1.7059 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
29 ÷ 19 = 1.5263 - This has a remainder. 19 is not a factor.
29 ÷ 23 = 1.2609 - This has a remainder. 23 is not a factor.
29 ÷ 29 = 1 - No remainder! 29 is one of the factors!

The orange divisor(s) above are the prime factors of the number 13,882,880. 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 5 x 11 x 17 x 29 = 13,882,880. It can also be written in exponential form as 29 x 51 x 111 x 171 x 291.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 13,882,880.

13,882,880
Factor Arrows
26,941,440
Factor Arrows
23,470,720
Factor Arrows
21,735,360
Factor Arrows
2867,680
Factor Arrows
2433,840
Factor Arrows
2216,920
Factor Arrows
2108,460
Factor Arrows
254,230
Factor Arrows
227,115
Factor Arrows
55,423
Factor Arrows
11493
Factor Arrows
1729

More Prime Factorization Examples

13,882,87813,882,87913,882,88113,882,882
21 x 32 x 1271 x 6,073113,882,879131 x 371 x 1811 x 691121 x 131 x 191 x 1571 x 1791

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