Q: What is the prime factorization of the number 9,274,272?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 3 x 7 x 37 x 373
    • or also written as { 2, 2, 2, 2, 2, 3, 7, 37, 373 }
  • Written in exponential form: 25 x 31 x 71 x 371 x 3731

Why is the prime factorization of 9,274,272 written as 25 x 31 x 71 x 371 x 3731?

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 9,274,272

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 9,274,272 by 2

9,274,272 ÷ 2 = 4,637,136 - No remainder! 2 is one of the factors!
4,637,136 ÷ 2 = 2,318,568 - No remainder! 2 is one of the factors!
2,318,568 ÷ 2 = 1,159,284 - No remainder! 2 is one of the factors!
1,159,284 ÷ 2 = 579,642 - No remainder! 2 is one of the factors!
579,642 ÷ 2 = 289,821 - No remainder! 2 is one of the factors!
289,821 ÷ 2 = 144,910.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
289,821 ÷ 3 = 96,607 - No remainder! 3 is one of the factors!
96,607 ÷ 3 = 32,202.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
96,607 ÷ 5 = 19,321.4 - This has a remainder. 5 is not a factor.
96,607 ÷ 7 = 13,801 - No remainder! 7 is one of the factors!
13,801 ÷ 7 = 1,971.5714 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
13,801 ÷ 11 = 1,254.6364 - This has a remainder. 11 is not a factor.
13,801 ÷ 13 = 1,061.6154 - This has a remainder. 13 is not a factor.
13,801 ÷ 17 = 811.8235 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
13,801 ÷ 37 = 373 - No remainder! 37 is one of the factors!
373 ÷ 37 = 10.0811 - There is a remainder. We can't divide by 37 evenly anymore. Let's try the next prime number
373 ÷ 41 = 9.0976 - This has a remainder. 41 is not a factor.
373 ÷ 43 = 8.6744 - This has a remainder. 43 is not a factor.
373 ÷ 47 = 7.9362 - This has a remainder. 47 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
373 ÷ 373 = 1 - No remainder! 373 is one of the factors!

The orange divisor(s) above are the prime factors of the number 9,274,272. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 3 x 7 x 37 x 373 = 9,274,272. It can also be written in exponential form as 25 x 31 x 71 x 371 x 3731.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 9,274,272.

9,274,272
Factor Arrows
24,637,136
Factor Arrows
22,318,568
Factor Arrows
21,159,284
Factor Arrows
2579,642
Factor Arrows
2289,821
Factor Arrows
396,607
Factor Arrows
713,801
Factor Arrows
37373

More Prime Factorization Examples

9,274,2709,274,2719,274,2739,274,274
21 x 51 x 311 x 29,91712291 x 40,49919,274,273121 x 672 x 1,0331

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