Alright folks, let’s break down how I tackled finding the prime factors of 650 today. Needed to do this for something else and figured why not share the messy process? No fancy math degrees here, just basic stuff.
Grabbed a Pen and Paper
Started simple. Wrote down the number: 650. Stared at it. Honestly? Felt big. Brain went blank for a sec. Where to even begin?
Then I remembered the oldest trick: divide by small numbers. Super obvious, right? But that’s where you start. My first target? 2. Is 650 even? Yep, ends with a zero. Easy. So I wrote:
- 650 ÷ 2 = 325
Okay, progress. Now I had 325 staring back at me.
Stuck on the Next Step
Tried dividing 325 by 2 again. Nope. Not even. Fine. Next up: 3. Added the digits: 3 + 2 + 5 = 10. Is 10 divisible by 3? Nope. 325 stayed stubborn.
Moved to 5. Every number ending in 0 or 5 plays nice with 5. And bingo: 325 ends with 5. Divided it:
- 325 ÷ 5 = 65
Better! Now I was down to 65. Smaller number feels less scary.
Back to Small Numbers Again
What divides into 65? Checked 2. No, it’s odd. Tried 3: 6 + 5 = 11. Not divisible by 3. Nope. So, back to trusty 5. 65 ends with 5? Absolutely. Divided:
- 65 ÷ 5 = 13
Boom. 13. Felt familiar. Is 13 a prime number? Yup. Can’t divide it further except by 1 and itself. Done with dividing.
Putting the Puzzle Pieces Together
So, I gathered all the numbers I used to divide:
- Started with ÷ 2 → Got 325
- Then ÷ 5 → Got 65
- Then ÷ 5 again → Got 13
- And 13 is prime.
Wrote those divisors down in order: 2, 5, 5, and the leftover prime 13.
Double-checked. Multiplied them together: 2 × 5 = 10, then 10 × 5 = 50, then 50 × 13. Grabbed the calculator… 650. Perfect. It worked.
So that’s it! The prime factorization of 650 is really just multiplying those smaller prime numbers I found:
2 × 5 × 5 × 13. Sometimes you see it written as 2 × 5² × 13. But honestly, listing them out is fine by me.
Not rocket science, just dividing step by step with the small primes till you hit paydirt. Glad I kept scratching my head and trying those little numbers!
