Alright, so today I had a bit of a math moment, you know? Decided to find the greatest common factor, or GCF as some folks call it, for 32 and 80. Thought I’d share how I went about it, just my practical way of doing things.
First things first, I took the number 32. I just started thinking, what numbers divide evenly into 32? It’s usually how I start with these things, just listing them out.
Let’s see…
- 1, definitely. Because 1 times 32 is 32.
- 2, yep. That goes in, 2 times 16.
- 3? Nah, 3 doesn’t go into 32 evenly.
- 4? Sure, 4 times 8. That’s a clear one.
- 5? Nope, not for 32.
- 6? Doesn’t work.
- 8? Yeah, we already got that with 4 times 8, so we are seeing pairs.
So, after puzzling it out, the factors for 32 I jotted down were 1, 2, 4, 8, 16, and 32. Got them all lined up. Pretty straightforward, actually.
Breaking down 80
Next up was 80. A bit of a bigger number, but I just followed the same idea. No need to complicate things.
So, for 80, I started listing again:
- 1, always a starter. 1 times 80. Easy.
- 2, yep, that’s an even number. 2 times 40.
- 3? Nope, 8 plus 0 is 8, and 3 doesn’t go into 8.
- 4? Yes, 4 times 20. That works.
- 5? Definitely, because it ends in a 0. So, 5 times 16.
- 6? Let’s check… it’s divisible by 2 but not by 3, so no, 6 is out.
- 7? Nah, doesn’t feel right and a quick check confirms.
- 8? Yes, 8 times 10. That’s another pair.
- 10? Got that already with 8.
My list for 80, after going through it, looked like this: 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80. This one took a few more steps, a few more checks, but got there in the end.
Okay, now I had my two lists of factors, all written down.
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Then, the next part was to look for the numbers that were sitting in both lists. I just went through them one by one.
Let’s see…
1 is common, of course.
2 is common.
4 is in both.
8 is also in both lists.
And hey, 16 is common too! That’s interesting.
20 isn’t in the 32 list. 32 isn’t in the 80 list for common factors other than these.
So the common ones are 1, 2, 4, 8, and 16.
The biggest one of these common factors? Well, looking at that little group, it’s clearly 16.
So, there you have it. The GCF of 32 and 80, using my simple listing method, turned out to be 16. Sometimes the old ways, just writing things down and comparing, are the easiest to just get done, you know? No fancy calculators or complicated formulas for this one, just figuring it out step by step. That’s how I roll with these little challenges. Felt good to work it through!
