Q: What is the prime factorization of the number 302,707,712?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 17 x 17,389
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 17, 17,389 }
  • Written in exponential form: 210 x 171 x 17,3891

Why is the prime factorization of 302,707,712 written as 210 x 171 x 17,3891?

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 302,707,712

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 302,707,712 by 2

302,707,712 ÷ 2 = 151,353,856 - No remainder! 2 is one of the factors!
151,353,856 ÷ 2 = 75,676,928 - No remainder! 2 is one of the factors!
75,676,928 ÷ 2 = 37,838,464 - No remainder! 2 is one of the factors!
37,838,464 ÷ 2 = 18,919,232 - No remainder! 2 is one of the factors!
18,919,232 ÷ 2 = 9,459,616 - No remainder! 2 is one of the factors!
9,459,616 ÷ 2 = 4,729,808 - No remainder! 2 is one of the factors!
4,729,808 ÷ 2 = 2,364,904 - No remainder! 2 is one of the factors!
2,364,904 ÷ 2 = 1,182,452 - No remainder! 2 is one of the factors!
1,182,452 ÷ 2 = 591,226 - No remainder! 2 is one of the factors!
591,226 ÷ 2 = 295,613 - No remainder! 2 is one of the factors!
295,613 ÷ 2 = 147,806.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
295,613 ÷ 3 = 98,537.6667 - This has a remainder. 3 is not a factor.
295,613 ÷ 5 = 59,122.6 - This has a remainder. 5 is not a factor.
295,613 ÷ 7 = 42,230.4286 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
295,613 ÷ 17 = 17,389 - No remainder! 17 is one of the factors!
17,389 ÷ 17 = 1,022.8824 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
17,389 ÷ 19 = 915.2105 - This has a remainder. 19 is not a factor.
17,389 ÷ 23 = 756.0435 - This has a remainder. 23 is not a factor.
17,389 ÷ 29 = 599.6207 - This has a remainder. 29 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
17,389 ÷ 17,389 = 1 - No remainder! 17,389 is one of the factors!

The orange divisor(s) above are the prime factors of the number 302,707,712. 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 2 x 17 x 17,389 = 302,707,712. It can also be written in exponential form as 210 x 171 x 17,3891.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 302,707,712.

302,707,712
Factor Arrows
2151,353,856
Factor Arrows
275,676,928
Factor Arrows
237,838,464
Factor Arrows
218,919,232
Factor Arrows
29,459,616
Factor Arrows
24,729,808
Factor Arrows
22,364,904
Factor Arrows
21,182,452
Factor Arrows
2591,226
Factor Arrows
2295,613
Factor Arrows
1717,389

More Prime Factorization Examples

302,707,710302,707,711302,707,713302,707,714
21 x 32 x 51 x 3,363,419111,9871 x 25,253131 x 71 x 111 x 291 x 731 x 619121 x 7,5591 x 20,0231

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