Q: What is the prime factorization of the number 616,960?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 241
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 241 }
  • Written in exponential form: 29 x 51 x 2411

Why is the prime factorization of 616,960 written as 29 x 51 x 2411?

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 616,960

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 616,960 by 2

616,960 ÷ 2 = 308,480 - No remainder! 2 is one of the factors!
308,480 ÷ 2 = 154,240 - No remainder! 2 is one of the factors!
154,240 ÷ 2 = 77,120 - No remainder! 2 is one of the factors!
77,120 ÷ 2 = 38,560 - No remainder! 2 is one of the factors!
38,560 ÷ 2 = 19,280 - No remainder! 2 is one of the factors!
19,280 ÷ 2 = 9,640 - No remainder! 2 is one of the factors!
9,640 ÷ 2 = 4,820 - No remainder! 2 is one of the factors!
4,820 ÷ 2 = 2,410 - No remainder! 2 is one of the factors!
2,410 ÷ 2 = 1,205 - No remainder! 2 is one of the factors!
1,205 ÷ 2 = 602.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
1,205 ÷ 3 = 401.6667 - This has a remainder. 3 is not a factor.
1,205 ÷ 5 = 241 - No remainder! 5 is one of the factors!
241 ÷ 5 = 48.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
241 ÷ 7 = 34.4286 - This has a remainder. 7 is not a factor.
241 ÷ 11 = 21.9091 - This has a remainder. 11 is not a factor.
241 ÷ 13 = 18.5385 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
241 ÷ 241 = 1 - No remainder! 241 is one of the factors!

The orange divisor(s) above are the prime factors of the number 616,960. 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 5 x 241 = 616,960. It can also be written in exponential form as 29 x 51 x 2411.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 616,960.

616,960
Factor Arrows
2308,480
Factor Arrows
2154,240
Factor Arrows
277,120
Factor Arrows
238,560
Factor Arrows
219,280
Factor Arrows
29,640
Factor Arrows
24,820
Factor Arrows
22,410
Factor Arrows
21,205
Factor Arrows
5241

More Prime Factorization Examples

616,958616,959616,961616,962
21 x 2511 x 1,229132 x 72 x 1,3991616,961121 x 31 x 312 x 1071

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