Q: What is the prime factorization of the number 47,683,328?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 x 11 x 41 x 59
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 7, 11, 41, 59 }
  • Written in exponential form: 28 x 71 x 111 x 411 x 591

Why is the prime factorization of 47,683,328 written as 28 x 71 x 111 x 411 x 591?

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 47,683,328

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 47,683,328 by 2

47,683,328 ÷ 2 = 23,841,664 - No remainder! 2 is one of the factors!
23,841,664 ÷ 2 = 11,920,832 - No remainder! 2 is one of the factors!
11,920,832 ÷ 2 = 5,960,416 - No remainder! 2 is one of the factors!
5,960,416 ÷ 2 = 2,980,208 - No remainder! 2 is one of the factors!
2,980,208 ÷ 2 = 1,490,104 - No remainder! 2 is one of the factors!
1,490,104 ÷ 2 = 745,052 - No remainder! 2 is one of the factors!
745,052 ÷ 2 = 372,526 - No remainder! 2 is one of the factors!
372,526 ÷ 2 = 186,263 - No remainder! 2 is one of the factors!
186,263 ÷ 2 = 93,131.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
186,263 ÷ 3 = 62,087.6667 - This has a remainder. 3 is not a factor.
186,263 ÷ 5 = 37,252.6 - This has a remainder. 5 is not a factor.
186,263 ÷ 7 = 26,609 - No remainder! 7 is one of the factors!
26,609 ÷ 7 = 3,801.2857 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
26,609 ÷ 11 = 2,419 - No remainder! 11 is one of the factors!
2,419 ÷ 11 = 219.9091 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
2,419 ÷ 13 = 186.0769 - This has a remainder. 13 is not a factor.
2,419 ÷ 17 = 142.2941 - This has a remainder. 17 is not a factor.
2,419 ÷ 19 = 127.3158 - This has a remainder. 19 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,419 ÷ 41 = 59 - No remainder! 41 is one of the factors!
59 ÷ 41 = 1.439 - There is a remainder. We can't divide by 41 evenly anymore. Let's try the next prime number
59 ÷ 43 = 1.3721 - This has a remainder. 43 is not a factor.
59 ÷ 47 = 1.2553 - This has a remainder. 47 is not a factor.
59 ÷ 53 = 1.1132 - This has a remainder. 53 is not a factor.
59 ÷ 59 = 1 - No remainder! 59 is one of the factors!

The orange divisor(s) above are the prime factors of the number 47,683,328. 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 2 x 7 x 11 x 41 x 59 = 47,683,328. It can also be written in exponential form as 28 x 71 x 111 x 411 x 591.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 47,683,328.

47,683,328
Factor Arrows
223,841,664
Factor Arrows
211,920,832
Factor Arrows
25,960,416
Factor Arrows
22,980,208
Factor Arrows
21,490,104
Factor Arrows
2745,052
Factor Arrows
2372,526
Factor Arrows
2186,263
Factor Arrows
726,609
Factor Arrows
112,419
Factor Arrows
4159

More Prime Factorization Examples

47,683,32647,683,32747,683,32947,683,330
21 x 31 x 7,947,221147,683,327131 x 1,5431 x 10,301121 x 51 x 1,6691 x 2,8571

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