Q: What is the prime factorization of the number 5,160,960?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 7 }
  • Written in exponential form: 214 x 32 x 51 x 71

Why is the prime factorization of 5,160,960 written as 214 x 32 x 51 x 71?

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 5,160,960

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 5,160,960 by 2

5,160,960 ÷ 2 = 2,580,480 - No remainder! 2 is one of the factors!
2,580,480 ÷ 2 = 1,290,240 - No remainder! 2 is one of the factors!
1,290,240 ÷ 2 = 645,120 - No remainder! 2 is one of the factors!
645,120 ÷ 2 = 322,560 - No remainder! 2 is one of the factors!
322,560 ÷ 2 = 161,280 - No remainder! 2 is one of the factors!
161,280 ÷ 2 = 80,640 - No remainder! 2 is one of the factors!
80,640 ÷ 2 = 40,320 - No remainder! 2 is one of the factors!
40,320 ÷ 2 = 20,160 - No remainder! 2 is one of the factors!
20,160 ÷ 2 = 10,080 - No remainder! 2 is one of the factors!
10,080 ÷ 2 = 5,040 - No remainder! 2 is one of the factors!
5,040 ÷ 2 = 2,520 - No remainder! 2 is one of the factors!
2,520 ÷ 2 = 1,260 - No remainder! 2 is one of the factors!
1,260 ÷ 2 = 630 - No remainder! 2 is one of the factors!
630 ÷ 2 = 315 - No remainder! 2 is one of the factors!
315 ÷ 2 = 157.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
315 ÷ 3 = 105 - No remainder! 3 is one of the factors!
105 ÷ 3 = 35 - No remainder! 3 is one of the factors!
35 ÷ 3 = 11.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
35 ÷ 5 = 7 - No remainder! 5 is one of the factors!
7 ÷ 5 = 1.4 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
7 ÷ 7 = 1 - No remainder! 7 is one of the factors!

The orange divisor(s) above are the prime factors of the number 5,160,960. 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 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 = 5,160,960. It can also be written in exponential form as 214 x 32 x 51 x 71.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 5,160,960.

5,160,960
Factor Arrows
22,580,480
Factor Arrows
21,290,240
Factor Arrows
2645,120
Factor Arrows
2322,560
Factor Arrows
2161,280
Factor Arrows
280,640
Factor Arrows
240,320
Factor Arrows
220,160
Factor Arrows
210,080
Factor Arrows
25,040
Factor Arrows
22,520
Factor Arrows
21,260
Factor Arrows
2630
Factor Arrows
2315
Factor Arrows
3105
Factor Arrows
335
Factor Arrows
57

More Prime Factorization Examples

5,160,9585,160,9595,160,9615,160,962
21 x 111 x 234,58915,160,9591131 x 396,997121 x 172 x 8,9291

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