Q: What is the prime factorization of the number 745,068,847?

 A:
  • The prime factors are: 26,641 x 27,967
    • or also written as { 26,641, 27,967 }
  • Written in exponential form: 26,6411 x 27,9671

Why is the prime factorization of 745,068,847 written as 26,6411 x 27,9671?

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 745,068,847

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 745,068,847 by 2

745,068,847 ÷ 2 = 372,534,423.5 - This has a remainder. Let's try another prime number.
745,068,847 ÷ 3 = 248,356,282.3333 - This has a remainder. Let's try another prime number.
745,068,847 ÷ 5 = 149,013,769.4 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
745,068,847 ÷ 26,641 = 27,967 - No remainder! 26,641 is one of the factors!
27,967 ÷ 26,641 = 1.0498 - There is a remainder. We can't divide by 26641 evenly anymore. Let's try the next prime number
27,967 ÷ 26,647 = 1.0495 - This has a remainder. 26,647 is not a factor.
27,967 ÷ 26,669 = 1.0487 - This has a remainder. 26,669 is not a factor.
27,967 ÷ 26,681 = 1.0482 - This has a remainder. 26,681 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
27,967 ÷ 27,967 = 1 - No remainder! 27,967 is one of the factors!

The orange divisor(s) above are the prime factors of the number 745,068,847. If we put all of it together we have the factors 26,641 x 27,967 = 745,068,847. It can also be written in exponential form as 26,6411 x 27,9671.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 745,068,847.

745,068,847
Factor Arrows
26,64127,967

More Prime Factorization Examples

745,068,845745,068,846745,068,848745,068,849
51 x 7331 x 203,293121 x 31 x 1091 x 1,139,249124 x 46,566,803131 x 71 x 311 x 1,144,4991

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