Q: What is the prime factorization of the number 1,050,672?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 3 x 7 x 53 x 59
    • or also written as { 2, 2, 2, 2, 3, 7, 53, 59 }
  • Written in exponential form: 24 x 31 x 71 x 531 x 591

Why is the prime factorization of 1,050,672 written as 24 x 31 x 71 x 531 x 591?

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 1,050,672

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 1,050,672 by 2

1,050,672 ÷ 2 = 525,336 - No remainder! 2 is one of the factors!
525,336 ÷ 2 = 262,668 - No remainder! 2 is one of the factors!
262,668 ÷ 2 = 131,334 - No remainder! 2 is one of the factors!
131,334 ÷ 2 = 65,667 - No remainder! 2 is one of the factors!
65,667 ÷ 2 = 32,833.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
65,667 ÷ 3 = 21,889 - No remainder! 3 is one of the factors!
21,889 ÷ 3 = 7,296.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
21,889 ÷ 5 = 4,377.8 - This has a remainder. 5 is not a factor.
21,889 ÷ 7 = 3,127 - No remainder! 7 is one of the factors!
3,127 ÷ 7 = 446.7143 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
3,127 ÷ 11 = 284.2727 - This has a remainder. 11 is not a factor.
3,127 ÷ 13 = 240.5385 - This has a remainder. 13 is not a factor.
3,127 ÷ 17 = 183.9412 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
3,127 ÷ 53 = 59 - No remainder! 53 is one of the factors!
59 ÷ 53 = 1.1132 - There is a remainder. We can't divide by 53 evenly anymore. Let's try the next prime number
59 ÷ 59 = 1 - No remainder! 59 is one of the factors!

The orange divisor(s) above are the prime factors of the number 1,050,672. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 3 x 7 x 53 x 59 = 1,050,672. It can also be written in exponential form as 24 x 31 x 71 x 531 x 591.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 1,050,672.

1,050,672
Factor Arrows
2525,336
Factor Arrows
2262,668
Factor Arrows
2131,334
Factor Arrows
265,667
Factor Arrows
321,889
Factor Arrows
73,127
Factor Arrows
5359

More Prime Factorization Examples

1,050,6701,050,6711,050,6731,050,674
21 x 51 x 291 x 3,62311271 x 8,2731132 x 6,217121 x 1131 x 4,6491

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