Q: What is the prime factorization of the number 520,530,432?

 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 113 x 2,999
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 113, 2,999 }
  • Written in exponential form: 29 x 31 x 1131 x 2,9991

Why is the prime factorization of 520,530,432 written as 29 x 31 x 1131 x 2,9991?

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 520,530,432

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 520,530,432 by 2

520,530,432 ÷ 2 = 260,265,216 - No remainder! 2 is one of the factors!
260,265,216 ÷ 2 = 130,132,608 - No remainder! 2 is one of the factors!
130,132,608 ÷ 2 = 65,066,304 - No remainder! 2 is one of the factors!
65,066,304 ÷ 2 = 32,533,152 - No remainder! 2 is one of the factors!
32,533,152 ÷ 2 = 16,266,576 - No remainder! 2 is one of the factors!
16,266,576 ÷ 2 = 8,133,288 - No remainder! 2 is one of the factors!
8,133,288 ÷ 2 = 4,066,644 - No remainder! 2 is one of the factors!
4,066,644 ÷ 2 = 2,033,322 - No remainder! 2 is one of the factors!
2,033,322 ÷ 2 = 1,016,661 - No remainder! 2 is one of the factors!
1,016,661 ÷ 2 = 508,330.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
1,016,661 ÷ 3 = 338,887 - No remainder! 3 is one of the factors!
338,887 ÷ 3 = 112,962.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
338,887 ÷ 5 = 67,777.4 - This has a remainder. 5 is not a factor.
338,887 ÷ 7 = 48,412.4286 - This has a remainder. 7 is not a factor.
338,887 ÷ 11 = 30,807.9091 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
338,887 ÷ 113 = 2,999 - No remainder! 113 is one of the factors!
2,999 ÷ 113 = 26.5398 - There is a remainder. We can't divide by 113 evenly anymore. Let's try the next prime number
2,999 ÷ 127 = 23.6142 - This has a remainder. 127 is not a factor.
2,999 ÷ 131 = 22.8931 - This has a remainder. 131 is not a factor.
2,999 ÷ 137 = 21.8905 - This has a remainder. 137 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,999 ÷ 2,999 = 1 - No remainder! 2,999 is one of the factors!

The orange divisor(s) above are the prime factors of the number 520,530,432. 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 113 x 2,999 = 520,530,432. It can also be written in exponential form as 29 x 31 x 1131 x 2,9991.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 520,530,432.

520,530,432
Factor Arrows
2260,265,216
Factor Arrows
2130,132,608
Factor Arrows
265,066,304
Factor Arrows
232,533,152
Factor Arrows
216,266,576
Factor Arrows
28,133,288
Factor Arrows
24,066,644
Factor Arrows
22,033,322
Factor Arrows
21,016,661
Factor Arrows
3338,887
Factor Arrows
1132,999

More Prime Factorization Examples

520,530,430520,530,431520,530,433520,530,434
21 x 51 x 72 x 371 x 28,7111520,530,4311831 x 1,9791 x 3,169121 x 231 x 1,5111 x 7,4891

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