Q: What is the prime factorization of the number 6,284,288?

 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 17 x 19 x 19
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 17, 19, 19 }
  • Written in exponential form: 210 x 171 x 192

Why is the prime factorization of 6,284,288 written as 210 x 171 x 192?

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 6,284,288

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 6,284,288 by 2

6,284,288 ÷ 2 = 3,142,144 - No remainder! 2 is one of the factors!
3,142,144 ÷ 2 = 1,571,072 - No remainder! 2 is one of the factors!
1,571,072 ÷ 2 = 785,536 - No remainder! 2 is one of the factors!
785,536 ÷ 2 = 392,768 - No remainder! 2 is one of the factors!
392,768 ÷ 2 = 196,384 - No remainder! 2 is one of the factors!
196,384 ÷ 2 = 98,192 - No remainder! 2 is one of the factors!
98,192 ÷ 2 = 49,096 - No remainder! 2 is one of the factors!
49,096 ÷ 2 = 24,548 - No remainder! 2 is one of the factors!
24,548 ÷ 2 = 12,274 - No remainder! 2 is one of the factors!
12,274 ÷ 2 = 6,137 - No remainder! 2 is one of the factors!
6,137 ÷ 2 = 3,068.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
6,137 ÷ 3 = 2,045.6667 - This has a remainder. 3 is not a factor.
6,137 ÷ 5 = 1,227.4 - This has a remainder. 5 is not a factor.
6,137 ÷ 7 = 876.7143 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
6,137 ÷ 17 = 361 - No remainder! 17 is one of the factors!
361 ÷ 17 = 21.2353 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
361 ÷ 19 = 19 - No remainder! 19 is one of the factors!
19 ÷ 19 = 1 - No remainder! 19 is one of the factors!

The orange divisor(s) above are the prime factors of the number 6,284,288. 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 17 x 19 x 19 = 6,284,288. It can also be written in exponential form as 210 x 171 x 192.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 6,284,288.

6,284,288
Factor Arrows
23,142,144
Factor Arrows
21,571,072
Factor Arrows
2785,536
Factor Arrows
2392,768
Factor Arrows
2196,384
Factor Arrows
298,192
Factor Arrows
249,096
Factor Arrows
224,548
Factor Arrows
212,274
Factor Arrows
26,137
Factor Arrows
17361
Factor Arrows
1919

More Prime Factorization Examples

6,284,2866,284,2876,284,2896,284,290
21 x 32 x 1091 x 3,20312511 x 25,037131 x 111 x 311 x 6,143121 x 51 x 231 x 891 x 3071

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