Q: What is the prime factorization of the number 72,050,686?

 A:
  • The prime factors are: 2 x 79 x 593 x 769
    • or also written as { 2, 79, 593, 769 }
  • Written in exponential form: 21 x 791 x 5931 x 7691

Why is the prime factorization of 72,050,686 written as 21 x 791 x 5931 x 7691?

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 72,050,686

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 72,050,686 by 2

72,050,686 ÷ 2 = 36,025,343 - No remainder! 2 is one of the factors!
36,025,343 ÷ 2 = 18,012,671.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
36,025,343 ÷ 3 = 12,008,447.6667 - This has a remainder. 3 is not a factor.
36,025,343 ÷ 5 = 7,205,068.6 - This has a remainder. 5 is not a factor.
36,025,343 ÷ 7 = 5,146,477.5714 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
36,025,343 ÷ 79 = 456,017 - No remainder! 79 is one of the factors!
456,017 ÷ 79 = 5,772.3671 - There is a remainder. We can't divide by 79 evenly anymore. Let's try the next prime number
456,017 ÷ 83 = 5,494.1807 - This has a remainder. 83 is not a factor.
456,017 ÷ 89 = 5,123.7865 - This has a remainder. 89 is not a factor.
456,017 ÷ 97 = 4,701.2062 - This has a remainder. 97 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
456,017 ÷ 593 = 769 - No remainder! 593 is one of the factors!
769 ÷ 593 = 1.2968 - There is a remainder. We can't divide by 593 evenly anymore. Let's try the next prime number
769 ÷ 599 = 1.2838 - This has a remainder. 599 is not a factor.
769 ÷ 601 = 1.2795 - This has a remainder. 601 is not a factor.
769 ÷ 607 = 1.2669 - This has a remainder. 607 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
769 ÷ 769 = 1 - No remainder! 769 is one of the factors!

The orange divisor(s) above are the prime factors of the number 72,050,686. If we put all of it together we have the factors 2 x 79 x 593 x 769 = 72,050,686. It can also be written in exponential form as 21 x 791 x 5931 x 7691.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 72,050,686.

72,050,686
Factor Arrows
236,025,343
Factor Arrows
79456,017
Factor Arrows
593769

More Prime Factorization Examples

72,050,68472,050,68572,050,68772,050,688
22 x 18,012,671131 x 51 x 71 x 686,19711,4931 x 48,2591211 x 33 x 1,3031

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