Q: What is the prime factorization of the number 641,984?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 7 x 1,433
    • or also written as { 2, 2, 2, 2, 2, 2, 7, 1,433 }
  • Written in exponential form: 26 x 71 x 1,4331

Why is the prime factorization of 641,984 written as 26 x 71 x 1,4331?

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 641,984

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 641,984 by 2

641,984 ÷ 2 = 320,992 - No remainder! 2 is one of the factors!
320,992 ÷ 2 = 160,496 - No remainder! 2 is one of the factors!
160,496 ÷ 2 = 80,248 - No remainder! 2 is one of the factors!
80,248 ÷ 2 = 40,124 - No remainder! 2 is one of the factors!
40,124 ÷ 2 = 20,062 - No remainder! 2 is one of the factors!
20,062 ÷ 2 = 10,031 - No remainder! 2 is one of the factors!
10,031 ÷ 2 = 5,015.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
10,031 ÷ 3 = 3,343.6667 - This has a remainder. 3 is not a factor.
10,031 ÷ 5 = 2,006.2 - This has a remainder. 5 is not a factor.
10,031 ÷ 7 = 1,433 - No remainder! 7 is one of the factors!
1,433 ÷ 7 = 204.7143 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
1,433 ÷ 11 = 130.2727 - This has a remainder. 11 is not a factor.
1,433 ÷ 13 = 110.2308 - This has a remainder. 13 is not a factor.
1,433 ÷ 17 = 84.2941 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
1,433 ÷ 1,433 = 1 - No remainder! 1,433 is one of the factors!

The orange divisor(s) above are the prime factors of the number 641,984. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 7 x 1,433 = 641,984. It can also be written in exponential form as 26 x 71 x 1,4331.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 641,984.

641,984
Factor Arrows
2320,992
Factor Arrows
2160,496
Factor Arrows
280,248
Factor Arrows
240,124
Factor Arrows
220,062
Factor Arrows
210,031
Factor Arrows
71,433

More Prime Factorization Examples

641,982641,983641,985641,986
21 x 31 x 111 x 711 x 13712631 x 2,441131 x 51 x 1271 x 337121 x 2571 x 1,2491

Try the factor calculator

Explore more about the number 641,984:


Ask a Question