Getting Started with 135
Alright, so today I decided to tackle this thing, the prime factorization of 135. Sounded straightforward, but you know, sometimes these simple things have a way of making you think. So, I just sat down and thought, “Okay, how do I break this number down into its prime bits?”
My First Steps and Thoughts
First thing that popped into my head was, “Start small.” The smallest prime number is 2, right? So I went, “Is 135 divisible by 2?” Nah, it’s an odd number, ends in a 5. So, 2 was out of the picture pretty quick. No sweat.
Next up was 3. “Okay, what about 3?” I remembered that trick: add up the digits. 1 + 3 + 5 equals 9. And 9 is divisible by 3. Bingo! So, 135 had to be divisible by 3. I grabbed my mental calculator (or, okay, maybe a piece of paper, who am I kidding?) and did the division: 135 divided by 3. That gave me 45. Cool, so 3 is one of our prime factors. I jotted that down.
Digging Deeper
Now I was looking at 45. I thought, “Let’s try 3 again with this new number.” Can 45 be divided by 3? 4 + 5 is 9. Yep, 9 is divisible by 3 again. So, 45 divided by 3 is 15. Awesome! Another 3 for my list of factors. Now I’m down to 15.
So, with 15, I did the same thing. “Can 15 be divided by 3?” 1 + 5 is 6. And 6 is divisible by 3. You bet! 15 divided by 3 is 5. So, another 3. Man, this number 135 really likes 3.
The Final Piece
Now I was left with 5. “Okay, can 5 be divided by 3?” Nope, clearly not. So, I moved on to the next prime number after 3, which is 5. “Is 5 divisible by 5?” Well, duh, of course it is! 5 divided by 5 is 1. And when you hit 1, you’re done. That means 5 is my last prime factor.
Putting It All Together
So, I looked at all the factors I’d collected. I had:
- A 3 from 135 / 3 = 45
- Another 3 from 45 / 3 = 15
- One more 3 from 15 / 3 = 5
- And finally, a 5 from 5 / 5 = 1
So, the prime factors of 135 are 3, 3, 3, and 5. If you want to write it out, 135 = 3 x 3 x 3 x 5. Or, you know, 3 to the power of 3 times 5. 3³ x 5. That felt pretty good, actually. Just chipping away at it until it was all broken down. Not too shabby for a bit of number work.
