Q: What is the prime factorization of the number 11,686,380?

 A:
  • The prime factors are: 2 x 2 x 3 x 5 x 31 x 61 x 103
    • or also written as { 2, 2, 3, 5, 31, 61, 103 }
  • Written in exponential form: 22 x 31 x 51 x 311 x 611 x 1031

Why is the prime factorization of 11,686,380 written as 22 x 31 x 51 x 311 x 611 x 1031?

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 11,686,380

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 11,686,380 by 2

11,686,380 ÷ 2 = 5,843,190 - No remainder! 2 is one of the factors!
5,843,190 ÷ 2 = 2,921,595 - No remainder! 2 is one of the factors!
2,921,595 ÷ 2 = 1,460,797.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
2,921,595 ÷ 3 = 973,865 - No remainder! 3 is one of the factors!
973,865 ÷ 3 = 324,621.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
973,865 ÷ 5 = 194,773 - No remainder! 5 is one of the factors!
194,773 ÷ 5 = 38,954.6 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
194,773 ÷ 7 = 27,824.7143 - This has a remainder. 7 is not a factor.
194,773 ÷ 11 = 17,706.6364 - This has a remainder. 11 is not a factor.
194,773 ÷ 13 = 14,982.5385 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
194,773 ÷ 31 = 6,283 - No remainder! 31 is one of the factors!
6,283 ÷ 31 = 202.6774 - There is a remainder. We can't divide by 31 evenly anymore. Let's try the next prime number
6,283 ÷ 37 = 169.8108 - This has a remainder. 37 is not a factor.
6,283 ÷ 41 = 153.2439 - This has a remainder. 41 is not a factor.
6,283 ÷ 43 = 146.1163 - This has a remainder. 43 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
6,283 ÷ 61 = 103 - No remainder! 61 is one of the factors!
103 ÷ 61 = 1.6885 - There is a remainder. We can't divide by 61 evenly anymore. Let's try the next prime number
103 ÷ 67 = 1.5373 - This has a remainder. 67 is not a factor.
103 ÷ 71 = 1.4507 - This has a remainder. 71 is not a factor.
103 ÷ 73 = 1.411 - This has a remainder. 73 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
103 ÷ 103 = 1 - No remainder! 103 is one of the factors!

The orange divisor(s) above are the prime factors of the number 11,686,380. If we put all of it together we have the factors 2 x 2 x 3 x 5 x 31 x 61 x 103 = 11,686,380. It can also be written in exponential form as 22 x 31 x 51 x 311 x 611 x 1031.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 11,686,380.

11,686,380
Factor Arrows
25,843,190
Factor Arrows
22,921,595
Factor Arrows
3973,865
Factor Arrows
5194,773
Factor Arrows
316,283
Factor Arrows
61103

More Prime Factorization Examples

11,686,37811,686,37911,686,38111,686,382
21 x 111 x 171 x 31,24711311 x 89,209171 x 3671 x 4,549121 x 5,843,1911

Try the factor calculator

Explore more about the number 11,686,380:


Ask a Question