Q: What is the prime factorization of the number 7,527,936?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 13 x 29
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 13, 13, 29 }
  • Written in exponential form: 29 x 31 x 132 x 291

Why is the prime factorization of 7,527,936 written as 29 x 31 x 132 x 291?

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 7,527,936

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 7,527,936 by 2

7,527,936 ÷ 2 = 3,763,968 - No remainder! 2 is one of the factors!
3,763,968 ÷ 2 = 1,881,984 - No remainder! 2 is one of the factors!
1,881,984 ÷ 2 = 940,992 - No remainder! 2 is one of the factors!
940,992 ÷ 2 = 470,496 - No remainder! 2 is one of the factors!
470,496 ÷ 2 = 235,248 - No remainder! 2 is one of the factors!
235,248 ÷ 2 = 117,624 - No remainder! 2 is one of the factors!
117,624 ÷ 2 = 58,812 - No remainder! 2 is one of the factors!
58,812 ÷ 2 = 29,406 - No remainder! 2 is one of the factors!
29,406 ÷ 2 = 14,703 - No remainder! 2 is one of the factors!
14,703 ÷ 2 = 7,351.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
14,703 ÷ 3 = 4,901 - No remainder! 3 is one of the factors!
4,901 ÷ 3 = 1,633.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
4,901 ÷ 5 = 980.2 - This has a remainder. 5 is not a factor.
4,901 ÷ 7 = 700.1429 - This has a remainder. 7 is not a factor.
4,901 ÷ 11 = 445.5455 - This has a remainder. 11 is not a factor.
4,901 ÷ 13 = 377 - No remainder! 13 is one of the factors!
377 ÷ 13 = 29 - No remainder! 13 is one of the factors!
29 ÷ 13 = 2.2308 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
29 ÷ 17 = 1.7059 - This has a remainder. 17 is not a factor.
29 ÷ 19 = 1.5263 - This has a remainder. 19 is not a factor.
29 ÷ 23 = 1.2609 - This has a remainder. 23 is not a factor.
29 ÷ 29 = 1 - No remainder! 29 is one of the factors!

The orange divisor(s) above are the prime factors of the number 7,527,936. 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 3 x 13 x 13 x 29 = 7,527,936. It can also be written in exponential form as 29 x 31 x 132 x 291.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 7,527,936.

7,527,936
Factor Arrows
23,763,968
Factor Arrows
21,881,984
Factor Arrows
2940,992
Factor Arrows
2470,496
Factor Arrows
2235,248
Factor Arrows
2117,624
Factor Arrows
258,812
Factor Arrows
229,406
Factor Arrows
214,703
Factor Arrows
34,901
Factor Arrows
13377
Factor Arrows
1329

More Prime Factorization Examples

7,527,9347,527,9357,527,9377,527,938
21 x 831 x 1011 x 449151 x 1,505,58711,1531 x 6,529121 x 111 x 342,1791

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