Q: What is the prime factorization of the number 26,604,032?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 x 13 x 571
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 13, 571 }
  • Written in exponential form: 29 x 71 x 131 x 5711

Why is the prime factorization of 26,604,032 written as 29 x 71 x 131 x 5711?

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 26,604,032

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 26,604,032 by 2

26,604,032 ÷ 2 = 13,302,016 - No remainder! 2 is one of the factors!
13,302,016 ÷ 2 = 6,651,008 - No remainder! 2 is one of the factors!
6,651,008 ÷ 2 = 3,325,504 - No remainder! 2 is one of the factors!
3,325,504 ÷ 2 = 1,662,752 - No remainder! 2 is one of the factors!
1,662,752 ÷ 2 = 831,376 - No remainder! 2 is one of the factors!
831,376 ÷ 2 = 415,688 - No remainder! 2 is one of the factors!
415,688 ÷ 2 = 207,844 - No remainder! 2 is one of the factors!
207,844 ÷ 2 = 103,922 - No remainder! 2 is one of the factors!
103,922 ÷ 2 = 51,961 - No remainder! 2 is one of the factors!
51,961 ÷ 2 = 25,980.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
51,961 ÷ 3 = 17,320.3333 - This has a remainder. 3 is not a factor.
51,961 ÷ 5 = 10,392.2 - This has a remainder. 5 is not a factor.
51,961 ÷ 7 = 7,423 - No remainder! 7 is one of the factors!
7,423 ÷ 7 = 1,060.4286 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
7,423 ÷ 11 = 674.8182 - This has a remainder. 11 is not a factor.
7,423 ÷ 13 = 571 - No remainder! 13 is one of the factors!
571 ÷ 13 = 43.9231 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
571 ÷ 17 = 33.5882 - This has a remainder. 17 is not a factor.
571 ÷ 19 = 30.0526 - This has a remainder. 19 is not a factor.
571 ÷ 23 = 24.8261 - This has a remainder. 23 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
571 ÷ 571 = 1 - No remainder! 571 is one of the factors!

The orange divisor(s) above are the prime factors of the number 26,604,032. 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 2 x 7 x 13 x 571 = 26,604,032. It can also be written in exponential form as 29 x 71 x 131 x 5711.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 26,604,032.

26,604,032
Factor Arrows
213,302,016
Factor Arrows
26,651,008
Factor Arrows
23,325,504
Factor Arrows
21,662,752
Factor Arrows
2831,376
Factor Arrows
2415,688
Factor Arrows
2207,844
Factor Arrows
2103,922
Factor Arrows
251,961
Factor Arrows
77,423
Factor Arrows
13571

More Prime Factorization Examples

26,604,03026,604,03126,604,03326,604,034
21 x 31 x 51 x 1371 x 6,4731171 x 231 x 68,041131 x 8,868,011121 x 1,9971 x 6,6611

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