Q: What is the prime factorization of the number 33,785,667?

 A:
  • The prime factors are: 3 x 3 x 3 x 3 x 19 x 29 x 757
    • or also written as { 3, 3, 3, 3, 19, 29, 757 }
  • Written in exponential form: 34 x 191 x 291 x 7571

Why is the prime factorization of 33,785,667 written as 34 x 191 x 291 x 7571?

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 33,785,667

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 33,785,667 by 2

33,785,667 ÷ 2 = 16,892,833.5 - This has a remainder. Let's try another prime number.
33,785,667 ÷ 3 = 11,261,889 - No remainder! 3 is one of the factors!
11,261,889 ÷ 3 = 3,753,963 - No remainder! 3 is one of the factors!
3,753,963 ÷ 3 = 1,251,321 - No remainder! 3 is one of the factors!
1,251,321 ÷ 3 = 417,107 - No remainder! 3 is one of the factors!
417,107 ÷ 3 = 139,035.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
417,107 ÷ 5 = 83,421.4 - This has a remainder. 5 is not a factor.
417,107 ÷ 7 = 59,586.7143 - This has a remainder. 7 is not a factor.
417,107 ÷ 11 = 37,918.8182 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
417,107 ÷ 19 = 21,953 - No remainder! 19 is one of the factors!
21,953 ÷ 19 = 1,155.4211 - There is a remainder. We can't divide by 19 evenly anymore. Let's try the next prime number
21,953 ÷ 23 = 954.4783 - This has a remainder. 23 is not a factor.
21,953 ÷ 29 = 757 - No remainder! 29 is one of the factors!
757 ÷ 29 = 26.1034 - There is a remainder. We can't divide by 29 evenly anymore. Let's try the next prime number
757 ÷ 31 = 24.4194 - This has a remainder. 31 is not a factor.
757 ÷ 37 = 20.4595 - This has a remainder. 37 is not a factor.
757 ÷ 41 = 18.4634 - This has a remainder. 41 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
757 ÷ 757 = 1 - No remainder! 757 is one of the factors!

The orange divisor(s) above are the prime factors of the number 33,785,667. If we put all of it together we have the factors 3 x 3 x 3 x 3 x 19 x 29 x 757 = 33,785,667. It can also be written in exponential form as 34 x 191 x 291 x 7571.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 33,785,667.

33,785,667
Factor Arrows
311,261,889
Factor Arrows
33,753,963
Factor Arrows
31,251,321
Factor Arrows
3417,107
Factor Arrows
1921,953
Factor Arrows
29757

More Prime Factorization Examples

33,785,66533,785,66633,785,66833,785,669
51 x 6,757,133121 x 231 x 734,471122 x 71 x 471 x 25,67311,3011 x 25,9691

Try the factor calculator

Explore more about the number 33,785,667:


Ask a Question