Q: What is the prime factorization of the number 6,210,048?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 311
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 13, 311 }
  • Written in exponential form: 29 x 31 x 131 x 3111

Why is the prime factorization of 6,210,048 written as 29 x 31 x 131 x 3111?

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 6,210,048

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 6,210,048 by 2

6,210,048 ÷ 2 = 3,105,024 - No remainder! 2 is one of the factors!
3,105,024 ÷ 2 = 1,552,512 - No remainder! 2 is one of the factors!
1,552,512 ÷ 2 = 776,256 - No remainder! 2 is one of the factors!
776,256 ÷ 2 = 388,128 - No remainder! 2 is one of the factors!
388,128 ÷ 2 = 194,064 - No remainder! 2 is one of the factors!
194,064 ÷ 2 = 97,032 - No remainder! 2 is one of the factors!
97,032 ÷ 2 = 48,516 - No remainder! 2 is one of the factors!
48,516 ÷ 2 = 24,258 - No remainder! 2 is one of the factors!
24,258 ÷ 2 = 12,129 - No remainder! 2 is one of the factors!
12,129 ÷ 2 = 6,064.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
12,129 ÷ 3 = 4,043 - No remainder! 3 is one of the factors!
4,043 ÷ 3 = 1,347.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
4,043 ÷ 5 = 808.6 - This has a remainder. 5 is not a factor.
4,043 ÷ 7 = 577.5714 - This has a remainder. 7 is not a factor.
4,043 ÷ 11 = 367.5455 - This has a remainder. 11 is not a factor.
4,043 ÷ 13 = 311 - No remainder! 13 is one of the factors!
311 ÷ 13 = 23.9231 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
311 ÷ 17 = 18.2941 - This has a remainder. 17 is not a factor.
311 ÷ 19 = 16.3684 - This has a remainder. 19 is not a factor.
311 ÷ 23 = 13.5217 - This has a remainder. 23 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
311 ÷ 311 = 1 - No remainder! 311 is one of the factors!

The orange divisor(s) above are the prime factors of the number 6,210,048. 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 3 x 13 x 311 = 6,210,048. It can also be written in exponential form as 29 x 31 x 131 x 3111.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 6,210,048.

6,210,048
Factor Arrows
23,105,024
Factor Arrows
21,552,512
Factor Arrows
2776,256
Factor Arrows
2388,128
Factor Arrows
2194,064
Factor Arrows
297,032
Factor Arrows
248,516
Factor Arrows
224,258
Factor Arrows
212,129
Factor Arrows
34,043
Factor Arrows
13311

More Prime Factorization Examples

6,210,0466,210,0476,210,0496,210,050
21 x 231 x 1271 x 1,06311791 x 34,6931171 x 365,297121 x 52 x 71 x 111 x 1,6131

Try the factor calculator

Explore more about the number 6,210,048:


Ask a Question