Okay, so I was messing around with numbers today, and I got stuck on this “108 factored” thing. I’ve gotta break down 108 into its prime factors. Sounds simple, right? It kinda is, but I wanted to walk through it step-by-step, just to make sure I really got it.
First, I grabbed a piece of paper and a pen – yeah, I’m old school like that. I wrote down 108 at the top. Then, I started thinking: what’s the smallest prime number that goes into 108? Obviously, it’s 2, since 108 is even.
So, I divided 108 by 2 and got 54. I drew a little branch under the 108, with 2 on one side and 54 on the other. Like a little tree starting to grow.
Keep it going!
- Next, I looked at 54. Also even, so I divided it by 2 again. That gave me 27. Another branch! Now I’ve got 2, 2, and 27.
- 27 isn’t even, so 2 is out. I tried the next prime number, 3. And bingo! 27 divided by 3 is 9.
- 9 is easy – it’s just 3 times 3. So, I finished with two more 3s on the branches of my little factor tree.
Finally, I was there. I had these numbers at the end of all my branches: 2, 2, 3, 3, and 3. These are all prime numbers.
To get back to my original 108 is very simple. I need to multiplied them all together: 2 2 3 3 3 = 108. Just to make sure I double-checked it, and yep, it works!
So, 108 factored is 2 x 2 x 3 x 3 x 3. Or, if you wanna get fancy, you can write it as 22 x 33. I scribbled that down too, just to feel extra smart.
It’s a small thing, but it’s satisfying to break a number down like that. I feel I have strong control over my numbers. Hope this little walkthrough helps someone else out there!