Q: What is the prime factorization of the number 5,788,160?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 7 x 17 x 19
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7, 17, 19 }
  • Written in exponential form: 29 x 51 x 71 x 171 x 191

Why is the prime factorization of 5,788,160 written as 29 x 51 x 71 x 171 x 191?

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 5,788,160

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 5,788,160 by 2

5,788,160 ÷ 2 = 2,894,080 - No remainder! 2 is one of the factors!
2,894,080 ÷ 2 = 1,447,040 - No remainder! 2 is one of the factors!
1,447,040 ÷ 2 = 723,520 - No remainder! 2 is one of the factors!
723,520 ÷ 2 = 361,760 - No remainder! 2 is one of the factors!
361,760 ÷ 2 = 180,880 - No remainder! 2 is one of the factors!
180,880 ÷ 2 = 90,440 - No remainder! 2 is one of the factors!
90,440 ÷ 2 = 45,220 - No remainder! 2 is one of the factors!
45,220 ÷ 2 = 22,610 - No remainder! 2 is one of the factors!
22,610 ÷ 2 = 11,305 - No remainder! 2 is one of the factors!
11,305 ÷ 2 = 5,652.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
11,305 ÷ 3 = 3,768.3333 - This has a remainder. 3 is not a factor.
11,305 ÷ 5 = 2,261 - No remainder! 5 is one of the factors!
2,261 ÷ 5 = 452.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
2,261 ÷ 7 = 323 - No remainder! 7 is one of the factors!
323 ÷ 7 = 46.1429 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
323 ÷ 11 = 29.3636 - This has a remainder. 11 is not a factor.
323 ÷ 13 = 24.8462 - This has a remainder. 13 is not a factor.
323 ÷ 17 = 19 - No remainder! 17 is one of the factors!
19 ÷ 17 = 1.1176 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
19 ÷ 19 = 1 - No remainder! 19 is one of the factors!

The orange divisor(s) above are the prime factors of the number 5,788,160. 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 5 x 7 x 17 x 19 = 5,788,160. It can also be written in exponential form as 29 x 51 x 71 x 171 x 191.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 5,788,160.

5,788,160
Factor Arrows
22,894,080
Factor Arrows
21,447,040
Factor Arrows
2723,520
Factor Arrows
2361,760
Factor Arrows
2180,880
Factor Arrows
290,440
Factor Arrows
245,220
Factor Arrows
222,610
Factor Arrows
211,305
Factor Arrows
52,261
Factor Arrows
7323
Factor Arrows
1719

More Prime Factorization Examples

5,788,1585,788,1595,788,1615,788,162
21 x 31 x 964,6931131 x 5411 x 823132 x 643,129121 x 1,2311 x 2,3511

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