Q: What is the prime factorization of the number 46,030,764?

 A:
  • The prime factors are: 2 x 2 x 3 x 13 x 17 x 17 x 1,021
    • or also written as { 2, 2, 3, 13, 17, 17, 1,021 }
  • Written in exponential form: 22 x 31 x 131 x 172 x 1,0211

Why is the prime factorization of 46,030,764 written as 22 x 31 x 131 x 172 x 1,0211?

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 46,030,764

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 46,030,764 by 2

46,030,764 ÷ 2 = 23,015,382 - No remainder! 2 is one of the factors!
23,015,382 ÷ 2 = 11,507,691 - No remainder! 2 is one of the factors!
11,507,691 ÷ 2 = 5,753,845.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
11,507,691 ÷ 3 = 3,835,897 - No remainder! 3 is one of the factors!
3,835,897 ÷ 3 = 1,278,632.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
3,835,897 ÷ 5 = 767,179.4 - This has a remainder. 5 is not a factor.
3,835,897 ÷ 7 = 547,985.2857 - This has a remainder. 7 is not a factor.
3,835,897 ÷ 11 = 348,717.9091 - This has a remainder. 11 is not a factor.
3,835,897 ÷ 13 = 295,069 - No remainder! 13 is one of the factors!
295,069 ÷ 13 = 22,697.6154 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
295,069 ÷ 17 = 17,357 - No remainder! 17 is one of the factors!
17,357 ÷ 17 = 1,021 - No remainder! 17 is one of the factors!
1,021 ÷ 17 = 60.0588 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
1,021 ÷ 19 = 53.7368 - This has a remainder. 19 is not a factor.
1,021 ÷ 23 = 44.3913 - This has a remainder. 23 is not a factor.
1,021 ÷ 29 = 35.2069 - This has a remainder. 29 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
1,021 ÷ 1,021 = 1 - No remainder! 1,021 is one of the factors!

The orange divisor(s) above are the prime factors of the number 46,030,764. If we put all of it together we have the factors 2 x 2 x 3 x 13 x 17 x 17 x 1,021 = 46,030,764. It can also be written in exponential form as 22 x 31 x 131 x 172 x 1,0211.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 46,030,764.

46,030,764
Factor Arrows
223,015,382
Factor Arrows
211,507,691
Factor Arrows
33,835,897
Factor Arrows
13295,069
Factor Arrows
1717,357
Factor Arrows
171,021

More Prime Factorization Examples

46,030,76246,030,76346,030,76546,030,766
21 x 23,015,381146,030,763151 x 111 x 531 x 15,791121 x 471 x 489,6891

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