# Can 484/243 be simplified any more?

1. Nov 1, 2005

### Natasha1

Can 484/243 be simplified any more? Thanks

2. Nov 1, 2005

### Physics Monkey

What are the prime factors of 484 and 243?

3. Nov 1, 2005

### NateTG

Alternatively, do you know about Euclid's algorithm? (It's much faster and easier than prime factorization.)

4. Nov 1, 2005

I don't know

5. Nov 1, 2005

### Natasha1

Unfortunately not

6. Nov 1, 2005

### Gokul43201

Staff Emeritus
Natasha, did you read the rules for posting in this forum ? If you've forgotten them, please look them up in the sticky thread (found at the top of this forum) or in my signature line.

7. Nov 1, 2005

### Natasha1

Harsh

I mean I've devided all those numbers by their primes and I can't get it sorry

2 3 5 7 11 13 17 19 23 29
31 37 41 43 47 53 59 61 67 71
73 79 83 89 97 101 103 107 109 113
127 131 137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223 227 229
233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349
353 359 367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457 461 463
467 479 487

8. Nov 1, 2005

### StatusX

484 is really easy to factorize. You only get two prime factors. If neither of these divide 243, the fraction is in lowest terms.

9. Nov 1, 2005

### Gokul43201

Staff Emeritus
Tough, but them's the rules !

There's a better approach, in general, than grinding through all the primes. As Nate suggested above, you want to use Euclid's Algorithm to find the gcd of the two numbers.

http://www.cut-the-knot.org/blue/Euclid.shtml

10. Nov 1, 2005

### Natasha1

Thanks boss

I just don't get it though 484/2 = 242 but 243/2 = 121.5???

Their common prime is 241? So what does the fraction become?

Last edited: Nov 1, 2005
11. Nov 1, 2005

### Natasha1

Is it 1+ (241/243)?

Is it 1+ (241/243)?

12. Nov 1, 2005

### CarlB

$$484/243 = 2 - 2/243 = 2(1-3^{-5})$$

Carl

13. Nov 1, 2005

### Icebreaker

What you can do is google for a list of prime numbers, and see if the numerator or the denominator's on either one. And if you don't know Euclid's algorithm, try dividing by the primes instead of just some random integer.

Here's the first 1000: http://www.math.utah.edu/~alfeld/math/primelist.html

14. Nov 2, 2005

### Gokul43201

Staff Emeritus
You bet !

Common prime ? What's that ?

What do you want to do when to reduce a fraction to its lowest terms ?What you want is to be able to write 484/243 = a/b, where gcd(a,b) = 1.

This solution can be found simply by finding c = gcd(484,243), and then a= 484/c and b = 243/c.

If c=1, then the fraction is already in its simplest form.

PS : It'll take you no more than 5 minutes to learn Euclid's Algorithm.