Q: What is the prime factorization of the number 719,742?

 A:
  • The prime factors are: 2 x 3 x 139 x 863
    • or also written as { 2, 3, 139, 863 }
  • Written in exponential form: 21 x 31 x 1391 x 8631

Why is the prime factorization of 719,742 written as 21 x 31 x 1391 x 8631?

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 719,742

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 719,742 by 2

719,742 ÷ 2 = 359,871 - No remainder! 2 is one of the factors!
359,871 ÷ 2 = 179,935.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
359,871 ÷ 3 = 119,957 - No remainder! 3 is one of the factors!
119,957 ÷ 3 = 39,985.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
119,957 ÷ 5 = 23,991.4 - This has a remainder. 5 is not a factor.
119,957 ÷ 7 = 17,136.7143 - This has a remainder. 7 is not a factor.
119,957 ÷ 11 = 10,905.1818 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
119,957 ÷ 139 = 863 - No remainder! 139 is one of the factors!
863 ÷ 139 = 6.2086 - There is a remainder. We can't divide by 139 evenly anymore. Let's try the next prime number
863 ÷ 149 = 5.7919 - This has a remainder. 149 is not a factor.
863 ÷ 151 = 5.7152 - This has a remainder. 151 is not a factor.
863 ÷ 157 = 5.4968 - This has a remainder. 157 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
863 ÷ 863 = 1 - No remainder! 863 is one of the factors!

The orange divisor(s) above are the prime factors of the number 719,742. If we put all of it together we have the factors 2 x 3 x 139 x 863 = 719,742. It can also be written in exponential form as 21 x 31 x 1391 x 8631.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 719,742.

719,742
Factor Arrows
2359,871
Factor Arrows
3119,957
Factor Arrows
139863

More Prime Factorization Examples

719,740719,741719,743719,744
22 x 51 x 71 x 531 x 971111 x 591 x 1,1091891 x 8,087127 x 5,6231

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