Q: What is the prime factorization of the number 83,080,578?

 A:
  • The prime factors are: 2 x 3 x 7 x 7 x 19 x 107 x 139
    • or also written as { 2, 3, 7, 7, 19, 107, 139 }
  • Written in exponential form: 21 x 31 x 72 x 191 x 1071 x 1391

Why is the prime factorization of 83,080,578 written as 21 x 31 x 72 x 191 x 1071 x 1391?

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 83,080,578

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 83,080,578 by 2

83,080,578 ÷ 2 = 41,540,289 - No remainder! 2 is one of the factors!
41,540,289 ÷ 2 = 20,770,144.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
41,540,289 ÷ 3 = 13,846,763 - No remainder! 3 is one of the factors!
13,846,763 ÷ 3 = 4,615,587.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
13,846,763 ÷ 5 = 2,769,352.6 - This has a remainder. 5 is not a factor.
13,846,763 ÷ 7 = 1,978,109 - No remainder! 7 is one of the factors!
1,978,109 ÷ 7 = 282,587 - No remainder! 7 is one of the factors!
282,587 ÷ 7 = 40,369.5714 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
282,587 ÷ 11 = 25,689.7273 - This has a remainder. 11 is not a factor.
282,587 ÷ 13 = 21,737.4615 - This has a remainder. 13 is not a factor.
282,587 ÷ 17 = 16,622.7647 - This has a remainder. 17 is not a factor.
282,587 ÷ 19 = 14,873 - No remainder! 19 is one of the factors!
14,873 ÷ 19 = 782.7895 - There is a remainder. We can't divide by 19 evenly anymore. Let's try the next prime number
14,873 ÷ 23 = 646.6522 - This has a remainder. 23 is not a factor.
14,873 ÷ 29 = 512.8621 - This has a remainder. 29 is not a factor.
14,873 ÷ 31 = 479.7742 - This has a remainder. 31 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
14,873 ÷ 107 = 139 - No remainder! 107 is one of the factors!
139 ÷ 107 = 1.2991 - There is a remainder. We can't divide by 107 evenly anymore. Let's try the next prime number
139 ÷ 109 = 1.2752 - This has a remainder. 109 is not a factor.
139 ÷ 113 = 1.2301 - This has a remainder. 113 is not a factor.
139 ÷ 127 = 1.0945 - This has a remainder. 127 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
139 ÷ 139 = 1 - No remainder! 139 is one of the factors!

The orange divisor(s) above are the prime factors of the number 83,080,578. If we put all of it together we have the factors 2 x 3 x 7 x 7 x 19 x 107 x 139 = 83,080,578. It can also be written in exponential form as 21 x 31 x 72 x 191 x 1071 x 1391.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 83,080,578.

83,080,578
Factor Arrows
241,540,289
Factor Arrows
313,846,763
Factor Arrows
71,978,109
Factor Arrows
7282,587
Factor Arrows
1914,873
Factor Arrows
107139

More Prime Factorization Examples

83,080,57683,080,57783,080,57983,080,580
27 x 4331 x 1,4991231 x 371 x 2331 x 4191711 x 4091 x 2,861122 x 51 x 111 x 1011 x 3,7391

Try the factor calculator

Explore more about the number 83,080,578:


Ask a Question