Question

Explain how to find a prime factorization of a number!

Answer 1

Start with the number you need to find the prime factors for. Let's say your number 2,277.

2


Divide 2,277 by the first prime number (which is two). If 2 goes into 2,277 evenly, then you can break up the next number:

2,277 / 2 = 1,138.5

Therefore, 2 does not go in the number evenly. Try 3:

2,277 / 3 = 759

Three goes into 2,277 evenly, now work on 759.




3


Divide 759 by the smallest prime number. Two, again, does not go evenly into 759, so try 3:

759 / 3 = 253

Three goes into the number evenly, now work on 253.

4


Divide 253 by the smallest prime number. You'll notice that 253 doesn't go into any of the numbers except one:

253 / 11 = 23

Both 11 and 23 are prime numbers, which means you've (almost) come to the end of the road. Now you need to write the prime factors of 2,277 correctly.

5


Recall what numbers you used to factor the number 2,277: 3, 3, 11, 23. Mathematically, this is written as 3 x 3 x 11 x 23.

Now, reduce the 3 x 3 to 3 squared to get your final answer.

The prime factors are:

3^2 x 11 x 23