Q: What is the prime factorization of the number 244,343,246?

 A:
  • The prime factors are: 2 x 7 x 727 x 24,007
    • or also written as { 2, 7, 727, 24,007 }
  • Written in exponential form: 21 x 71 x 7271 x 24,0071

Why is the prime factorization of 244,343,246 written as 21 x 71 x 7271 x 24,0071?

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 244,343,246

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 244,343,246 by 2

244,343,246 ÷ 2 = 122,171,623 - No remainder! 2 is one of the factors!
122,171,623 ÷ 2 = 61,085,811.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
122,171,623 ÷ 3 = 40,723,874.3333 - This has a remainder. 3 is not a factor.
122,171,623 ÷ 5 = 24,434,324.6 - This has a remainder. 5 is not a factor.
122,171,623 ÷ 7 = 17,453,089 - No remainder! 7 is one of the factors!
17,453,089 ÷ 7 = 2,493,298.4286 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
17,453,089 ÷ 11 = 1,586,644.4545 - This has a remainder. 11 is not a factor.
17,453,089 ÷ 13 = 1,342,545.3077 - This has a remainder. 13 is not a factor.
17,453,089 ÷ 17 = 1,026,652.2941 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
17,453,089 ÷ 727 = 24,007 - No remainder! 727 is one of the factors!
24,007 ÷ 727 = 33.022 - There is a remainder. We can't divide by 727 evenly anymore. Let's try the next prime number
24,007 ÷ 733 = 32.7517 - This has a remainder. 733 is not a factor.
24,007 ÷ 739 = 32.4858 - This has a remainder. 739 is not a factor.
24,007 ÷ 743 = 32.3109 - This has a remainder. 743 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
24,007 ÷ 24,007 = 1 - No remainder! 24,007 is one of the factors!

The orange divisor(s) above are the prime factors of the number 244,343,246. If we put all of it together we have the factors 2 x 7 x 727 x 24,007 = 244,343,246. It can also be written in exponential form as 21 x 71 x 7271 x 24,0071.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 244,343,246.

244,343,246
Factor Arrows
2122,171,623
Factor Arrows
717,453,089
Factor Arrows
72724,007

More Prime Factorization Examples

244,343,244244,343,245244,343,247244,343,248
22 x 31 x 171 x 1911 x 6,271151 x 1,8711 x 26,119131 x 611 x 1,335,209124 x 2931 x 52,1211

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