Q: What is the prime factorization of the number 554,442,240?

 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 5 x 11 x 6,563
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 11, 6,563 }
  • Written in exponential form: 29 x 31 x 51 x 111 x 6,5631

Why is the prime factorization of 554,442,240 written as 29 x 31 x 51 x 111 x 6,5631?

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 554,442,240

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 554,442,240 by 2

554,442,240 ÷ 2 = 277,221,120 - No remainder! 2 is one of the factors!
277,221,120 ÷ 2 = 138,610,560 - No remainder! 2 is one of the factors!
138,610,560 ÷ 2 = 69,305,280 - No remainder! 2 is one of the factors!
69,305,280 ÷ 2 = 34,652,640 - No remainder! 2 is one of the factors!
34,652,640 ÷ 2 = 17,326,320 - No remainder! 2 is one of the factors!
17,326,320 ÷ 2 = 8,663,160 - No remainder! 2 is one of the factors!
8,663,160 ÷ 2 = 4,331,580 - No remainder! 2 is one of the factors!
4,331,580 ÷ 2 = 2,165,790 - No remainder! 2 is one of the factors!
2,165,790 ÷ 2 = 1,082,895 - No remainder! 2 is one of the factors!
1,082,895 ÷ 2 = 541,447.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
1,082,895 ÷ 3 = 360,965 - No remainder! 3 is one of the factors!
360,965 ÷ 3 = 120,321.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
360,965 ÷ 5 = 72,193 - No remainder! 5 is one of the factors!
72,193 ÷ 5 = 14,438.6 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
72,193 ÷ 7 = 10,313.2857 - This has a remainder. 7 is not a factor.
72,193 ÷ 11 = 6,563 - No remainder! 11 is one of the factors!
6,563 ÷ 11 = 596.6364 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
6,563 ÷ 13 = 504.8462 - This has a remainder. 13 is not a factor.
6,563 ÷ 17 = 386.0588 - This has a remainder. 17 is not a factor.
6,563 ÷ 19 = 345.4211 - This has a remainder. 19 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
6,563 ÷ 6,563 = 1 - No remainder! 6,563 is one of the factors!

The orange divisor(s) above are the prime factors of the number 554,442,240. 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 5 x 11 x 6,563 = 554,442,240. It can also be written in exponential form as 29 x 31 x 51 x 111 x 6,5631.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 554,442,240.

554,442,240
Factor Arrows
2277,221,120
Factor Arrows
2138,610,560
Factor Arrows
269,305,280
Factor Arrows
234,652,640
Factor Arrows
217,326,320
Factor Arrows
28,663,160
Factor Arrows
24,331,580
Factor Arrows
22,165,790
Factor Arrows
21,082,895
Factor Arrows
3360,965
Factor Arrows
572,193
Factor Arrows
116,563

More Prime Factorization Examples

554,442,238554,442,239554,442,241554,442,242
21 x 71 x 2391 x 165,7031131 x 42,649,4031831 x 6,680,027121 x 291 x 9,559,3491

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