Q: What is the prime factorization of the number 481,726,130?

 A:
  • The prime factors are: 2 x 5 x 941 x 51,193
    • or also written as { 2, 5, 941, 51,193 }
  • Written in exponential form: 21 x 51 x 9411 x 51,1931

Why is the prime factorization of 481,726,130 written as 21 x 51 x 9411 x 51,1931?

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 481,726,130

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 481,726,130 by 2

481,726,130 ÷ 2 = 240,863,065 - No remainder! 2 is one of the factors!
240,863,065 ÷ 2 = 120,431,532.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
240,863,065 ÷ 3 = 80,287,688.3333 - This has a remainder. 3 is not a factor.
240,863,065 ÷ 5 = 48,172,613 - No remainder! 5 is one of the factors!
48,172,613 ÷ 5 = 9,634,522.6 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
48,172,613 ÷ 7 = 6,881,801.8571 - This has a remainder. 7 is not a factor.
48,172,613 ÷ 11 = 4,379,328.4545 - This has a remainder. 11 is not a factor.
48,172,613 ÷ 13 = 3,705,585.6154 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
48,172,613 ÷ 941 = 51,193 - No remainder! 941 is one of the factors!
51,193 ÷ 941 = 54.4028 - There is a remainder. We can't divide by 941 evenly anymore. Let's try the next prime number
51,193 ÷ 947 = 54.0581 - This has a remainder. 947 is not a factor.
51,193 ÷ 953 = 53.7177 - This has a remainder. 953 is not a factor.
51,193 ÷ 967 = 52.94 - This has a remainder. 967 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
51,193 ÷ 51,193 = 1 - No remainder! 51,193 is one of the factors!

The orange divisor(s) above are the prime factors of the number 481,726,130. If we put all of it together we have the factors 2 x 5 x 941 x 51,193 = 481,726,130. It can also be written in exponential form as 21 x 51 x 9411 x 51,1931.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 481,726,130.

481,726,130
Factor Arrows
2240,863,065
Factor Arrows
548,172,613
Factor Arrows
94151,193

More Prime Factorization Examples

481,726,128481,726,129481,726,131481,726,132
24 x 31 x 131 x 771,9971481,726,129131 x 160,575,377122 x 120,431,5331

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