Q: What is the prime factorization of the number 131,401,216?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 256,643
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 256,643 }
  • Written in exponential form: 29 x 256,6431

Why is the prime factorization of 131,401,216 written as 29 x 256,6431?

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 131,401,216

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 131,401,216 by 2

131,401,216 ÷ 2 = 65,700,608 - No remainder! 2 is one of the factors!
65,700,608 ÷ 2 = 32,850,304 - No remainder! 2 is one of the factors!
32,850,304 ÷ 2 = 16,425,152 - No remainder! 2 is one of the factors!
16,425,152 ÷ 2 = 8,212,576 - No remainder! 2 is one of the factors!
8,212,576 ÷ 2 = 4,106,288 - No remainder! 2 is one of the factors!
4,106,288 ÷ 2 = 2,053,144 - No remainder! 2 is one of the factors!
2,053,144 ÷ 2 = 1,026,572 - No remainder! 2 is one of the factors!
1,026,572 ÷ 2 = 513,286 - No remainder! 2 is one of the factors!
513,286 ÷ 2 = 256,643 - No remainder! 2 is one of the factors!
256,643 ÷ 2 = 128,321.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
256,643 ÷ 3 = 85,547.6667 - This has a remainder. 3 is not a factor.
256,643 ÷ 5 = 51,328.6 - This has a remainder. 5 is not a factor.
256,643 ÷ 7 = 36,663.2857 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
256,643 ÷ 256,643 = 1 - No remainder! 256,643 is one of the factors!

The orange divisor(s) above are the prime factors of the number 131,401,216. 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 256,643 = 131,401,216. It can also be written in exponential form as 29 x 256,6431.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 131,401,216.

131,401,216
Factor Arrows
265,700,608
Factor Arrows
232,850,304
Factor Arrows
216,425,152
Factor Arrows
28,212,576
Factor Arrows
24,106,288
Factor Arrows
22,053,144
Factor Arrows
21,026,572
Factor Arrows
2513,286
Factor Arrows
2256,643

More Prime Factorization Examples

131,401,214131,401,215131,401,217131,401,218
21 x 71 x 2,6211 x 3,581132 x 51 x 111 x 1791 x 1,4831131,401,217121 x 31 x 132 x 129,5871

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