Q: What is the prime factorization of the number 8,053,760?

 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 5 x 11 x 11 x 13
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 11, 11, 13 }
  • Written in exponential form: 210 x 51 x 112 x 131

Why is the prime factorization of 8,053,760 written as 210 x 51 x 112 x 131?

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 8,053,760

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 8,053,760 by 2

8,053,760 ÷ 2 = 4,026,880 - No remainder! 2 is one of the factors!
4,026,880 ÷ 2 = 2,013,440 - No remainder! 2 is one of the factors!
2,013,440 ÷ 2 = 1,006,720 - No remainder! 2 is one of the factors!
1,006,720 ÷ 2 = 503,360 - No remainder! 2 is one of the factors!
503,360 ÷ 2 = 251,680 - No remainder! 2 is one of the factors!
251,680 ÷ 2 = 125,840 - No remainder! 2 is one of the factors!
125,840 ÷ 2 = 62,920 - No remainder! 2 is one of the factors!
62,920 ÷ 2 = 31,460 - No remainder! 2 is one of the factors!
31,460 ÷ 2 = 15,730 - No remainder! 2 is one of the factors!
15,730 ÷ 2 = 7,865 - No remainder! 2 is one of the factors!
7,865 ÷ 2 = 3,932.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
7,865 ÷ 3 = 2,621.6667 - This has a remainder. 3 is not a factor.
7,865 ÷ 5 = 1,573 - No remainder! 5 is one of the factors!
1,573 ÷ 5 = 314.6 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
1,573 ÷ 7 = 224.7143 - This has a remainder. 7 is not a factor.
1,573 ÷ 11 = 143 - No remainder! 11 is one of the factors!
143 ÷ 11 = 13 - No remainder! 11 is one of the factors!
13 ÷ 11 = 1.1818 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
13 ÷ 13 = 1 - No remainder! 13 is one of the factors!

The orange divisor(s) above are the prime factors of the number 8,053,760. 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 5 x 11 x 11 x 13 = 8,053,760. It can also be written in exponential form as 210 x 51 x 112 x 131.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 8,053,760.

8,053,760
Factor Arrows
24,026,880
Factor Arrows
22,013,440
Factor Arrows
21,006,720
Factor Arrows
2503,360
Factor Arrows
2251,680
Factor Arrows
2125,840
Factor Arrows
262,920
Factor Arrows
231,460
Factor Arrows
215,730
Factor Arrows
27,865
Factor Arrows
51,573
Factor Arrows
11143
Factor Arrows
1113

More Prime Factorization Examples

8,053,7588,053,7598,053,7618,053,762
21 x 32 x 191 x 23,549171 x 1,150,537131 x 2,684,587121 x 1,0911 x 3,6911

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