Q: What is the prime factorization of the number 4,773,248?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 89 x 419
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 89, 419 }
  • Written in exponential form: 27 x 891 x 4191

Why is the prime factorization of 4,773,248 written as 27 x 891 x 4191?

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 4,773,248

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 4,773,248 by 2

4,773,248 ÷ 2 = 2,386,624 - No remainder! 2 is one of the factors!
2,386,624 ÷ 2 = 1,193,312 - No remainder! 2 is one of the factors!
1,193,312 ÷ 2 = 596,656 - No remainder! 2 is one of the factors!
596,656 ÷ 2 = 298,328 - No remainder! 2 is one of the factors!
298,328 ÷ 2 = 149,164 - No remainder! 2 is one of the factors!
149,164 ÷ 2 = 74,582 - No remainder! 2 is one of the factors!
74,582 ÷ 2 = 37,291 - No remainder! 2 is one of the factors!
37,291 ÷ 2 = 18,645.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
37,291 ÷ 3 = 12,430.3333 - This has a remainder. 3 is not a factor.
37,291 ÷ 5 = 7,458.2 - This has a remainder. 5 is not a factor.
37,291 ÷ 7 = 5,327.2857 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
37,291 ÷ 89 = 419 - No remainder! 89 is one of the factors!
419 ÷ 89 = 4.7079 - There is a remainder. We can't divide by 89 evenly anymore. Let's try the next prime number
419 ÷ 97 = 4.3196 - This has a remainder. 97 is not a factor.
419 ÷ 101 = 4.1485 - This has a remainder. 101 is not a factor.
419 ÷ 103 = 4.068 - This has a remainder. 103 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
419 ÷ 419 = 1 - No remainder! 419 is one of the factors!

The orange divisor(s) above are the prime factors of the number 4,773,248. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 2 x 89 x 419 = 4,773,248. It can also be written in exponential form as 27 x 891 x 4191.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 4,773,248.

4,773,248
Factor Arrows
22,386,624
Factor Arrows
21,193,312
Factor Arrows
2596,656
Factor Arrows
2298,328
Factor Arrows
2149,164
Factor Arrows
274,582
Factor Arrows
237,291
Factor Arrows
89419

More Prime Factorization Examples

4,773,2464,773,2474,773,2494,773,250
21 x 31 x 2411 x 3,3011831 x 1311 x 439135 x 131 x 1,511121 x 53 x 611 x 3131

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