Q: What is the prime factorization of the number 1,837,920?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 547
    • or also written as { 2, 2, 2, 2, 2, 3, 5, 7, 547 }
  • Written in exponential form: 25 x 31 x 51 x 71 x 5471

Why is the prime factorization of 1,837,920 written as 25 x 31 x 51 x 71 x 5471?

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 1,837,920

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 1,837,920 by 2

1,837,920 ÷ 2 = 918,960 - No remainder! 2 is one of the factors!
918,960 ÷ 2 = 459,480 - No remainder! 2 is one of the factors!
459,480 ÷ 2 = 229,740 - No remainder! 2 is one of the factors!
229,740 ÷ 2 = 114,870 - No remainder! 2 is one of the factors!
114,870 ÷ 2 = 57,435 - No remainder! 2 is one of the factors!
57,435 ÷ 2 = 28,717.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
57,435 ÷ 3 = 19,145 - No remainder! 3 is one of the factors!
19,145 ÷ 3 = 6,381.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
19,145 ÷ 5 = 3,829 - No remainder! 5 is one of the factors!
3,829 ÷ 5 = 765.8 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
3,829 ÷ 7 = 547 - No remainder! 7 is one of the factors!
547 ÷ 7 = 78.1429 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
547 ÷ 11 = 49.7273 - This has a remainder. 11 is not a factor.
547 ÷ 13 = 42.0769 - This has a remainder. 13 is not a factor.
547 ÷ 17 = 32.1765 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
547 ÷ 547 = 1 - No remainder! 547 is one of the factors!

The orange divisor(s) above are the prime factors of the number 1,837,920. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 547 = 1,837,920. It can also be written in exponential form as 25 x 31 x 51 x 71 x 5471.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 1,837,920.

1,837,920
Factor Arrows
2918,960
Factor Arrows
2459,480
Factor Arrows
2229,740
Factor Arrows
2114,870
Factor Arrows
257,435
Factor Arrows
319,145
Factor Arrows
53,829
Factor Arrows
7547

More Prime Factorization Examples

1,837,9181,837,9191,837,9211,837,922
21 x 918,95911,837,9191171 x 731 x 1,481121 x 2711 x 3,3911

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