Q: What is the prime factorization of the number 57,109,248?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 x 3,541
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 3,541 }
  • Written in exponential form: 28 x 32 x 71 x 3,5411

Why is the prime factorization of 57,109,248 written as 28 x 32 x 71 x 3,5411?

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 57,109,248

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 57,109,248 by 2

57,109,248 ÷ 2 = 28,554,624 - No remainder! 2 is one of the factors!
28,554,624 ÷ 2 = 14,277,312 - No remainder! 2 is one of the factors!
14,277,312 ÷ 2 = 7,138,656 - No remainder! 2 is one of the factors!
7,138,656 ÷ 2 = 3,569,328 - No remainder! 2 is one of the factors!
3,569,328 ÷ 2 = 1,784,664 - No remainder! 2 is one of the factors!
1,784,664 ÷ 2 = 892,332 - No remainder! 2 is one of the factors!
892,332 ÷ 2 = 446,166 - No remainder! 2 is one of the factors!
446,166 ÷ 2 = 223,083 - No remainder! 2 is one of the factors!
223,083 ÷ 2 = 111,541.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
223,083 ÷ 3 = 74,361 - No remainder! 3 is one of the factors!
74,361 ÷ 3 = 24,787 - No remainder! 3 is one of the factors!
24,787 ÷ 3 = 8,262.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
24,787 ÷ 5 = 4,957.4 - This has a remainder. 5 is not a factor.
24,787 ÷ 7 = 3,541 - No remainder! 7 is one of the factors!
3,541 ÷ 7 = 505.8571 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
3,541 ÷ 11 = 321.9091 - This has a remainder. 11 is not a factor.
3,541 ÷ 13 = 272.3846 - This has a remainder. 13 is not a factor.
3,541 ÷ 17 = 208.2941 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
3,541 ÷ 3,541 = 1 - No remainder! 3,541 is one of the factors!

The orange divisor(s) above are the prime factors of the number 57,109,248. 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 2 x 3 x 3 x 7 x 3,541 = 57,109,248. It can also be written in exponential form as 28 x 32 x 71 x 3,5411.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 57,109,248.

57,109,248
Factor Arrows
228,554,624
Factor Arrows
214,277,312
Factor Arrows
27,138,656
Factor Arrows
23,569,328
Factor Arrows
21,784,664
Factor Arrows
2892,332
Factor Arrows
2446,166
Factor Arrows
2223,083
Factor Arrows
374,361
Factor Arrows
324,787
Factor Arrows
73,541

More Prime Factorization Examples

57,109,24657,109,24757,109,24957,109,250
21 x 431 x 664,0611131 x 4,393,0191531 x 1,077,533121 x 53 x 111 x 191 x 1,0931

Try the factor calculator

Explore more about the number 57,109,248:


Ask a Question