Q: What is the prime factorization of the number 1,315,716?

 A:
  • The prime factors are: 2 x 2 x 3 x 83 x 1,321
    • or also written as { 2, 2, 3, 83, 1,321 }
  • Written in exponential form: 22 x 31 x 831 x 1,3211

Why is the prime factorization of 1,315,716 written as 22 x 31 x 831 x 1,3211?

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 1,315,716

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 1,315,716 by 2

1,315,716 ÷ 2 = 657,858 - No remainder! 2 is one of the factors!
657,858 ÷ 2 = 328,929 - No remainder! 2 is one of the factors!
328,929 ÷ 2 = 164,464.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
328,929 ÷ 3 = 109,643 - No remainder! 3 is one of the factors!
109,643 ÷ 3 = 36,547.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
109,643 ÷ 5 = 21,928.6 - This has a remainder. 5 is not a factor.
109,643 ÷ 7 = 15,663.2857 - This has a remainder. 7 is not a factor.
109,643 ÷ 11 = 9,967.5455 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
109,643 ÷ 83 = 1,321 - No remainder! 83 is one of the factors!
1,321 ÷ 83 = 15.9157 - There is a remainder. We can't divide by 83 evenly anymore. Let's try the next prime number
1,321 ÷ 89 = 14.8427 - This has a remainder. 89 is not a factor.
1,321 ÷ 97 = 13.6186 - This has a remainder. 97 is not a factor.
1,321 ÷ 101 = 13.0792 - This has a remainder. 101 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
1,321 ÷ 1,321 = 1 - No remainder! 1,321 is one of the factors!

The orange divisor(s) above are the prime factors of the number 1,315,716. If we put all of it together we have the factors 2 x 2 x 3 x 83 x 1,321 = 1,315,716. It can also be written in exponential form as 22 x 31 x 831 x 1,3211.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 1,315,716.

1,315,716
Factor Arrows
2657,858
Factor Arrows
2328,929
Factor Arrows
3109,643
Factor Arrows
831,321

More Prime Factorization Examples

1,315,7141,315,7151,315,7171,315,718
21 x 431 x 15,299151 x 171 x 231 x 6731131 x 101,209121 x 471 x 13,9971

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