Q: What is the prime factorization of the number 937,650?

 A:
  • The prime factors are: 2 x 3 x 5 x 5 x 7 x 19 x 47
    • or also written as { 2, 3, 5, 5, 7, 19, 47 }
  • Written in exponential form: 21 x 31 x 52 x 71 x 191 x 471

Why is the prime factorization of 937,650 written as 21 x 31 x 52 x 71 x 191 x 471?

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 937,650

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 937,650 by 2

937,650 ÷ 2 = 468,825 - No remainder! 2 is one of the factors!
468,825 ÷ 2 = 234,412.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
468,825 ÷ 3 = 156,275 - No remainder! 3 is one of the factors!
156,275 ÷ 3 = 52,091.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
156,275 ÷ 5 = 31,255 - No remainder! 5 is one of the factors!
31,255 ÷ 5 = 6,251 - No remainder! 5 is one of the factors!
6,251 ÷ 5 = 1,250.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
6,251 ÷ 7 = 893 - No remainder! 7 is one of the factors!
893 ÷ 7 = 127.5714 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
893 ÷ 11 = 81.1818 - This has a remainder. 11 is not a factor.
893 ÷ 13 = 68.6923 - This has a remainder. 13 is not a factor.
893 ÷ 17 = 52.5294 - This has a remainder. 17 is not a factor.
893 ÷ 19 = 47 - No remainder! 19 is one of the factors!
47 ÷ 19 = 2.4737 - There is a remainder. We can't divide by 19 evenly anymore. Let's try the next prime number
47 ÷ 23 = 2.0435 - This has a remainder. 23 is not a factor.
47 ÷ 29 = 1.6207 - This has a remainder. 29 is not a factor.
47 ÷ 31 = 1.5161 - This has a remainder. 31 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
47 ÷ 47 = 1 - No remainder! 47 is one of the factors!

The orange divisor(s) above are the prime factors of the number 937,650. If we put all of it together we have the factors 2 x 3 x 5 x 5 x 7 x 19 x 47 = 937,650. It can also be written in exponential form as 21 x 31 x 52 x 71 x 191 x 471.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 937,650.

937,650
Factor Arrows
2468,825
Factor Arrows
3156,275
Factor Arrows
531,255
Factor Arrows
56,251
Factor Arrows
7893
Factor Arrows
1947

More Prime Factorization Examples

937,648937,649937,651937,652
24 x 58,60317731 x 1,2131111 x 131 x 791 x 83122 x 171 x 13,7891

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