Q: What is the prime factorization of the number 715,574,272?

 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 7 x 99,829
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 99,829 }
  • Written in exponential form: 210 x 71 x 99,8291

Why is the prime factorization of 715,574,272 written as 210 x 71 x 99,8291?

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 715,574,272

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 715,574,272 by 2

715,574,272 ÷ 2 = 357,787,136 - No remainder! 2 is one of the factors!
357,787,136 ÷ 2 = 178,893,568 - No remainder! 2 is one of the factors!
178,893,568 ÷ 2 = 89,446,784 - No remainder! 2 is one of the factors!
89,446,784 ÷ 2 = 44,723,392 - No remainder! 2 is one of the factors!
44,723,392 ÷ 2 = 22,361,696 - No remainder! 2 is one of the factors!
22,361,696 ÷ 2 = 11,180,848 - No remainder! 2 is one of the factors!
11,180,848 ÷ 2 = 5,590,424 - No remainder! 2 is one of the factors!
5,590,424 ÷ 2 = 2,795,212 - No remainder! 2 is one of the factors!
2,795,212 ÷ 2 = 1,397,606 - No remainder! 2 is one of the factors!
1,397,606 ÷ 2 = 698,803 - No remainder! 2 is one of the factors!
698,803 ÷ 2 = 349,401.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
698,803 ÷ 3 = 232,934.3333 - This has a remainder. 3 is not a factor.
698,803 ÷ 5 = 139,760.6 - This has a remainder. 5 is not a factor.
698,803 ÷ 7 = 99,829 - No remainder! 7 is one of the factors!
99,829 ÷ 7 = 14,261.2857 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
99,829 ÷ 11 = 9,075.3636 - This has a remainder. 11 is not a factor.
99,829 ÷ 13 = 7,679.1538 - This has a remainder. 13 is not a factor.
99,829 ÷ 17 = 5,872.2941 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
99,829 ÷ 99,829 = 1 - No remainder! 99,829 is one of the factors!

The orange divisor(s) above are the prime factors of the number 715,574,272. 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 7 x 99,829 = 715,574,272. It can also be written in exponential form as 210 x 71 x 99,8291.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 715,574,272.

715,574,272
Factor Arrows
2357,787,136
Factor Arrows
2178,893,568
Factor Arrows
289,446,784
Factor Arrows
244,723,392
Factor Arrows
222,361,696
Factor Arrows
211,180,848
Factor Arrows
25,590,424
Factor Arrows
22,795,212
Factor Arrows
21,397,606
Factor Arrows
2698,803
Factor Arrows
799,829

More Prime Factorization Examples

715,574,270715,574,271715,574,273715,574,274
21 x 51 x 1071 x 668,761131 x 311 x 411 x 671 x 2,80112831 x 2,528,531121 x 31 x 1,0871 x 109,7171

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