Q: What is the prime factorization of the number 107,777,052?

 A:
  • The prime factors are: 2 x 2 x 3 x 3 x 457 x 6,551
    • or also written as { 2, 2, 3, 3, 457, 6,551 }
  • Written in exponential form: 22 x 32 x 4571 x 6,5511

Why is the prime factorization of 107,777,052 written as 22 x 32 x 4571 x 6,5511?

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 107,777,052

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 107,777,052 by 2

107,777,052 ÷ 2 = 53,888,526 - No remainder! 2 is one of the factors!
53,888,526 ÷ 2 = 26,944,263 - No remainder! 2 is one of the factors!
26,944,263 ÷ 2 = 13,472,131.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
26,944,263 ÷ 3 = 8,981,421 - No remainder! 3 is one of the factors!
8,981,421 ÷ 3 = 2,993,807 - No remainder! 3 is one of the factors!
2,993,807 ÷ 3 = 997,935.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
2,993,807 ÷ 5 = 598,761.4 - This has a remainder. 5 is not a factor.
2,993,807 ÷ 7 = 427,686.7143 - This has a remainder. 7 is not a factor.
2,993,807 ÷ 11 = 272,164.2727 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,993,807 ÷ 457 = 6,551 - No remainder! 457 is one of the factors!
6,551 ÷ 457 = 14.3348 - There is a remainder. We can't divide by 457 evenly anymore. Let's try the next prime number
6,551 ÷ 461 = 14.2104 - This has a remainder. 461 is not a factor.
6,551 ÷ 463 = 14.149 - This has a remainder. 463 is not a factor.
6,551 ÷ 467 = 14.0278 - This has a remainder. 467 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
6,551 ÷ 6,551 = 1 - No remainder! 6,551 is one of the factors!

The orange divisor(s) above are the prime factors of the number 107,777,052. If we put all of it together we have the factors 2 x 2 x 3 x 3 x 457 x 6,551 = 107,777,052. It can also be written in exponential form as 22 x 32 x 4571 x 6,5511.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 107,777,052.

107,777,052
Factor Arrows
253,888,526
Factor Arrows
226,944,263
Factor Arrows
38,981,421
Factor Arrows
32,993,807
Factor Arrows
4576,551

More Prime Factorization Examples

107,777,050107,777,051107,777,053107,777,054
21 x 52 x 291 x 2391 x 31115471 x 197,0331107,777,053121 x 71 x 111 x 731 x 9,5871

Try the factor calculator

Explore more about the number 107,777,052:


Ask a Question