Can 484/243 be simplified any more?

  • Thread starter Natasha1
  • Start date
In summary, Euclid's algorithm is a faster and easier way to find the gcd of two numbers than trying to find their prime factors.
  • #1
Natasha1
493
9
Can 484/243 be simplified any more? Thanks
 
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  • #2
What are the prime factors of 484 and 243?
 
  • #3
Alternatively, do you know about Euclid's algorithm? (It's much faster and easier than prime factorization.)
 
  • #4
Physics Monkey said:
What are the prime factors of 484 and 243?

I don't know
 
  • #5
NateTG said:
Alternatively, do you know about Euclid's algorithm? (It's much faster and easier than prime factorization.)

Unfortunately not :cry:
 
  • #6
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
Gokul43201 said:
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.


Harsh :cry:

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
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
Natasha1 said:
Harsh :cry:
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
Gokul43201 said:
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


Thanks boss :wink:

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:
  • #11
Is it 1+ (241/243)?

Is it 1+ (241/243)?
 
  • #12
[tex]484/243 = 2 - 2/243 = 2(1-3^{-5})[/tex]

Carl
 
  • #13
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
Natasha1 said:
Thanks boss :wink:
You bet !

I just don't get it though 484/2 = 242 but 243/2 = 121.5?
Their common prime is 241?
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.
 

1. Can 484/243 be simplified any more?

Yes, 484/243 can be simplified further.

2. What is the simplified form of 484/243?

The simplified form of 484/243 is 2.

3. How do I simplify 484/243?

To simplify 484/243, you can divide both the numerator and denominator by their greatest common factor, which is 121. This results in the simplified form of 2.

4. Is 484/243 in its simplest form?

No, 484/243 is not in its simplest form. It can be further simplified to 2.

5. Why is it important to simplify fractions?

Simplifying fractions makes them easier to work with and understand. It also helps to compare and manipulate fractions accurately. In some cases, simplifying fractions can also help in finding the smallest common denominator.

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