Q: What is the prime factorization of the number 530,752,248?

 A:
  • The prime factors are: 2 x 2 x 2 x 3 x 3 x 13 x 137 x 4,139
    • or also written as { 2, 2, 2, 3, 3, 13, 137, 4,139 }
  • Written in exponential form: 23 x 32 x 131 x 1371 x 4,1391

Why is the prime factorization of 530,752,248 written as 23 x 32 x 131 x 1371 x 4,1391?

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 530,752,248

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 530,752,248 by 2

530,752,248 ÷ 2 = 265,376,124 - No remainder! 2 is one of the factors!
265,376,124 ÷ 2 = 132,688,062 - No remainder! 2 is one of the factors!
132,688,062 ÷ 2 = 66,344,031 - No remainder! 2 is one of the factors!
66,344,031 ÷ 2 = 33,172,015.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
66,344,031 ÷ 3 = 22,114,677 - No remainder! 3 is one of the factors!
22,114,677 ÷ 3 = 7,371,559 - No remainder! 3 is one of the factors!
7,371,559 ÷ 3 = 2,457,186.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
7,371,559 ÷ 5 = 1,474,311.8 - This has a remainder. 5 is not a factor.
7,371,559 ÷ 7 = 1,053,079.8571 - This has a remainder. 7 is not a factor.
7,371,559 ÷ 11 = 670,141.7273 - This has a remainder. 11 is not a factor.
7,371,559 ÷ 13 = 567,043 - No remainder! 13 is one of the factors!
567,043 ÷ 13 = 43,618.6923 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
567,043 ÷ 17 = 33,355.4706 - This has a remainder. 17 is not a factor.
567,043 ÷ 19 = 29,844.3684 - This has a remainder. 19 is not a factor.
567,043 ÷ 23 = 24,654.0435 - This has a remainder. 23 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
567,043 ÷ 137 = 4,139 - No remainder! 137 is one of the factors!
4,139 ÷ 137 = 30.2117 - There is a remainder. We can't divide by 137 evenly anymore. Let's try the next prime number
4,139 ÷ 139 = 29.777 - This has a remainder. 139 is not a factor.
4,139 ÷ 149 = 27.7785 - This has a remainder. 149 is not a factor.
4,139 ÷ 151 = 27.4106 - This has a remainder. 151 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
4,139 ÷ 4,139 = 1 - No remainder! 4,139 is one of the factors!

The orange divisor(s) above are the prime factors of the number 530,752,248. If we put all of it together we have the factors 2 x 2 x 2 x 3 x 3 x 13 x 137 x 4,139 = 530,752,248. It can also be written in exponential form as 23 x 32 x 131 x 1371 x 4,1391.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 530,752,248.

530,752,248
Factor Arrows
2265,376,124
Factor Arrows
2132,688,062
Factor Arrows
266,344,031
Factor Arrows
322,114,677
Factor Arrows
37,371,559
Factor Arrows
13567,043
Factor Arrows
1374,139

More Prime Factorization Examples

530,752,246530,752,247530,752,249530,752,250
21 x 265,376,1231471 x 11,292,6011530,752,249121 x 53 x 71 x 303,2871

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