Q: What is the prime factorization of the number 340,714,464?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 3 x 293 x 12,113
    • or also written as { 2, 2, 2, 2, 2, 3, 293, 12,113 }
  • Written in exponential form: 25 x 31 x 2931 x 12,1131

Why is the prime factorization of 340,714,464 written as 25 x 31 x 2931 x 12,1131?

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 340,714,464

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 340,714,464 by 2

340,714,464 ÷ 2 = 170,357,232 - No remainder! 2 is one of the factors!
170,357,232 ÷ 2 = 85,178,616 - No remainder! 2 is one of the factors!
85,178,616 ÷ 2 = 42,589,308 - No remainder! 2 is one of the factors!
42,589,308 ÷ 2 = 21,294,654 - No remainder! 2 is one of the factors!
21,294,654 ÷ 2 = 10,647,327 - No remainder! 2 is one of the factors!
10,647,327 ÷ 2 = 5,323,663.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
10,647,327 ÷ 3 = 3,549,109 - No remainder! 3 is one of the factors!
3,549,109 ÷ 3 = 1,183,036.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
3,549,109 ÷ 5 = 709,821.8 - This has a remainder. 5 is not a factor.
3,549,109 ÷ 7 = 507,015.5714 - This has a remainder. 7 is not a factor.
3,549,109 ÷ 11 = 322,646.2727 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
3,549,109 ÷ 293 = 12,113 - No remainder! 293 is one of the factors!
12,113 ÷ 293 = 41.3413 - There is a remainder. We can't divide by 293 evenly anymore. Let's try the next prime number
12,113 ÷ 307 = 39.456 - This has a remainder. 307 is not a factor.
12,113 ÷ 311 = 38.9486 - This has a remainder. 311 is not a factor.
12,113 ÷ 313 = 38.6997 - This has a remainder. 313 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
12,113 ÷ 12,113 = 1 - No remainder! 12,113 is one of the factors!

The orange divisor(s) above are the prime factors of the number 340,714,464. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 3 x 293 x 12,113 = 340,714,464. It can also be written in exponential form as 25 x 31 x 2931 x 12,1131.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 340,714,464.

340,714,464
Factor Arrows
2170,357,232
Factor Arrows
285,178,616
Factor Arrows
242,589,308
Factor Arrows
221,294,654
Factor Arrows
210,647,327
Factor Arrows
33,549,109
Factor Arrows
29312,113

More Prime Factorization Examples

340,714,462340,714,463340,714,465340,714,466
21 x 112 x 4011 x 3,5111371 x 611 x 150,959151 x 71 x 131 x 748,823121 x 9291 x 183,3771

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