Q: What is the prime factorization of the number 1,870,000?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 11 x 17
    • or also written as { 2, 2, 2, 2, 5, 5, 5, 5, 11, 17 }
  • Written in exponential form: 24 x 54 x 111 x 171

Why is the prime factorization of 1,870,000 written as 24 x 54 x 111 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 1,870,000

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 1,870,000 by 2

1,870,000 ÷ 2 = 935,000 - No remainder! 2 is one of the factors!
935,000 ÷ 2 = 467,500 - No remainder! 2 is one of the factors!
467,500 ÷ 2 = 233,750 - No remainder! 2 is one of the factors!
233,750 ÷ 2 = 116,875 - No remainder! 2 is one of the factors!
116,875 ÷ 2 = 58,437.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
116,875 ÷ 3 = 38,958.3333 - This has a remainder. 3 is not a factor.
116,875 ÷ 5 = 23,375 - No remainder! 5 is one of the factors!
23,375 ÷ 5 = 4,675 - No remainder! 5 is one of the factors!
4,675 ÷ 5 = 935 - No remainder! 5 is one of the factors!
935 ÷ 5 = 187 - No remainder! 5 is one of the factors!
187 ÷ 5 = 37.4 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
187 ÷ 7 = 26.7143 - This has a remainder. 7 is not a factor.
187 ÷ 11 = 17 - No remainder! 11 is one of the factors!
17 ÷ 11 = 1.5455 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
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 1,870,000. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 11 x 17 = 1,870,000. It can also be written in exponential form as 24 x 54 x 111 x 171.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 1,870,000.

1,870,000
Factor Arrows
2935,000
Factor Arrows
2467,500
Factor Arrows
2233,750
Factor Arrows
2116,875
Factor Arrows
523,375
Factor Arrows
54,675
Factor Arrows
5935
Factor Arrows
5187
Factor Arrows
1117

More Prime Factorization Examples

1,869,9981,869,9991,870,0011,870,002
21 x 131 x 711 x 1,013131 x 191 x 531 x 619171 x 267,143121 x 32 x 103,8891

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