Q: What is the prime factorization of the number 5,570,560?

 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 2 x 2 x 5 x 17
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 17 }
  • Written in exponential form: 216 x 51 x 171

Why is the prime factorization of 5,570,560 written as 216 x 51 x 171?

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 5,570,560

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 5,570,560 by 2

5,570,560 ÷ 2 = 2,785,280 - No remainder! 2 is one of the factors!
2,785,280 ÷ 2 = 1,392,640 - No remainder! 2 is one of the factors!
1,392,640 ÷ 2 = 696,320 - No remainder! 2 is one of the factors!
696,320 ÷ 2 = 348,160 - No remainder! 2 is one of the factors!
348,160 ÷ 2 = 174,080 - No remainder! 2 is one of the factors!
174,080 ÷ 2 = 87,040 - No remainder! 2 is one of the factors!
87,040 ÷ 2 = 43,520 - No remainder! 2 is one of the factors!
43,520 ÷ 2 = 21,760 - No remainder! 2 is one of the factors!
21,760 ÷ 2 = 10,880 - No remainder! 2 is one of the factors!
10,880 ÷ 2 = 5,440 - No remainder! 2 is one of the factors!
5,440 ÷ 2 = 2,720 - No remainder! 2 is one of the factors!
2,720 ÷ 2 = 1,360 - No remainder! 2 is one of the factors!
1,360 ÷ 2 = 680 - No remainder! 2 is one of the factors!
680 ÷ 2 = 340 - No remainder! 2 is one of the factors!
340 ÷ 2 = 170 - No remainder! 2 is one of the factors!
170 ÷ 2 = 85 - No remainder! 2 is one of the factors!
85 ÷ 2 = 42.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
85 ÷ 3 = 28.3333 - This has a remainder. 3 is not a factor.
85 ÷ 5 = 17 - No remainder! 5 is one of the factors!
17 ÷ 5 = 3.4 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
17 ÷ 7 = 2.4286 - This has a remainder. 7 is not a factor.
17 ÷ 11 = 1.5455 - This has a remainder. 11 is not a factor.
17 ÷ 13 = 1.3077 - This has a remainder. 13 is not a factor.
17 ÷ 17 = 1 - No remainder! 17 is one of the factors!

The orange divisor(s) above are the prime factors of the number 5,570,560. 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 2 x 2 x 5 x 17 = 5,570,560. It can also be written in exponential form as 216 x 51 x 171.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 5,570,560.

5,570,560
Factor Arrows
22,785,280
Factor Arrows
21,392,640
Factor Arrows
2696,320
Factor Arrows
2348,160
Factor Arrows
2174,080
Factor Arrows
287,040
Factor Arrows
243,520
Factor Arrows
221,760
Factor Arrows
210,880
Factor Arrows
25,440
Factor Arrows
22,720
Factor Arrows
21,360
Factor Arrows
2680
Factor Arrows
2340
Factor Arrows
2170
Factor Arrows
285
Factor Arrows
517

More Prime Factorization Examples

5,570,5585,570,5595,570,5615,570,562
21 x 71 x 397,897133 x 1931 x 1,06911131 x 49,297121 x 31 x 928,4271

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