Q: What is the prime factorization of the number 610,306,352?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 1,223 x 31,189
    • or also written as { 2, 2, 2, 2, 1,223, 31,189 }
  • Written in exponential form: 24 x 1,2231 x 31,1891

Why is the prime factorization of 610,306,352 written as 24 x 1,2231 x 31,1891?

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 610,306,352

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 610,306,352 by 2

610,306,352 ÷ 2 = 305,153,176 - No remainder! 2 is one of the factors!
305,153,176 ÷ 2 = 152,576,588 - No remainder! 2 is one of the factors!
152,576,588 ÷ 2 = 76,288,294 - No remainder! 2 is one of the factors!
76,288,294 ÷ 2 = 38,144,147 - No remainder! 2 is one of the factors!
38,144,147 ÷ 2 = 19,072,073.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
38,144,147 ÷ 3 = 12,714,715.6667 - This has a remainder. 3 is not a factor.
38,144,147 ÷ 5 = 7,628,829.4 - This has a remainder. 5 is not a factor.
38,144,147 ÷ 7 = 5,449,163.8571 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
38,144,147 ÷ 1,223 = 31,189 - No remainder! 1,223 is one of the factors!
31,189 ÷ 1,223 = 25.502 - There is a remainder. We can't divide by 1223 evenly anymore. Let's try the next prime number
31,189 ÷ 1,229 = 25.3775 - This has a remainder. 1,229 is not a factor.
31,189 ÷ 1,231 = 25.3363 - This has a remainder. 1,231 is not a factor.
31,189 ÷ 1,237 = 25.2134 - This has a remainder. 1,237 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
31,189 ÷ 31,189 = 1 - No remainder! 31,189 is one of the factors!

The orange divisor(s) above are the prime factors of the number 610,306,352. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 1,223 x 31,189 = 610,306,352. It can also be written in exponential form as 24 x 1,2231 x 31,1891.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 610,306,352.

610,306,352
Factor Arrows
2305,153,176
Factor Arrows
2152,576,588
Factor Arrows
276,288,294
Factor Arrows
238,144,147
Factor Arrows
1,22331,189

More Prime Factorization Examples

610,306,350610,306,351610,306,353610,306,354
21 x 31 x 52 x 671 x 60,7271610,306,351133 x 191 x 431 x 731 x 379121 x 71 x 4791 x 91,0091

Try the factor calculator

Explore more about the number 610,306,352:


Ask a Question