Q: What is the prime factorization of the number 16,023,552?

 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 3 x 163
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 163 }
  • Written in exponential form: 215 x 31 x 1631

Why is the prime factorization of 16,023,552 written as 215 x 31 x 1631?

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 16,023,552

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 16,023,552 by 2

16,023,552 ÷ 2 = 8,011,776 - No remainder! 2 is one of the factors!
8,011,776 ÷ 2 = 4,005,888 - No remainder! 2 is one of the factors!
4,005,888 ÷ 2 = 2,002,944 - No remainder! 2 is one of the factors!
2,002,944 ÷ 2 = 1,001,472 - No remainder! 2 is one of the factors!
1,001,472 ÷ 2 = 500,736 - No remainder! 2 is one of the factors!
500,736 ÷ 2 = 250,368 - No remainder! 2 is one of the factors!
250,368 ÷ 2 = 125,184 - No remainder! 2 is one of the factors!
125,184 ÷ 2 = 62,592 - No remainder! 2 is one of the factors!
62,592 ÷ 2 = 31,296 - No remainder! 2 is one of the factors!
31,296 ÷ 2 = 15,648 - No remainder! 2 is one of the factors!
15,648 ÷ 2 = 7,824 - No remainder! 2 is one of the factors!
7,824 ÷ 2 = 3,912 - No remainder! 2 is one of the factors!
3,912 ÷ 2 = 1,956 - No remainder! 2 is one of the factors!
1,956 ÷ 2 = 978 - No remainder! 2 is one of the factors!
978 ÷ 2 = 489 - No remainder! 2 is one of the factors!
489 ÷ 2 = 244.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
489 ÷ 3 = 163 - No remainder! 3 is one of the factors!
163 ÷ 3 = 54.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
163 ÷ 5 = 32.6 - This has a remainder. 5 is not a factor.
163 ÷ 7 = 23.2857 - This has a remainder. 7 is not a factor.
163 ÷ 11 = 14.8182 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
163 ÷ 163 = 1 - No remainder! 163 is one of the factors!

The orange divisor(s) above are the prime factors of the number 16,023,552. 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 3 x 163 = 16,023,552. It can also be written in exponential form as 215 x 31 x 1631.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 16,023,552.

16,023,552
Factor Arrows
28,011,776
Factor Arrows
24,005,888
Factor Arrows
22,002,944
Factor Arrows
21,001,472
Factor Arrows
2500,736
Factor Arrows
2250,368
Factor Arrows
2125,184
Factor Arrows
262,592
Factor Arrows
231,296
Factor Arrows
215,648
Factor Arrows
27,824
Factor Arrows
23,912
Factor Arrows
21,956
Factor Arrows
2978
Factor Arrows
2489
Factor Arrows
3163

More Prime Factorization Examples

16,023,55016,023,55116,023,55316,023,554
21 x 52 x 320,47112111 x 75,941171 x 131 x 371 x 4,759121 x 171 x 471,2811

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