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Number theory concept I can't understand. watch

1. I found it weird. Let's say "a" and "b" are 3 and 4 respectively.

How can I find a possible common divisor like that?

And, how does the first sentence link to the fact that "we can always assume that a given fraction is irreducible"?
2. What I understand it as is:

For example 6/8 = 3/4 [by dividing out 2 from the top and bottom]

3/4 we know is irreducible as gcd(3,4) = 1.

So 6/8 becomes irreducible.
3. (Original post by talissu160)

I found it weird. Let's say "a" and "b" are 3 and 4 respectively.

How can I find a possible common divisor like that?
It's badly worded. It's saying that if and have a common divisor greater than 1, then we can always find it and divide it out.

And, how does the first sentence link to the fact that "we can always assume that a given fraction is irreducible"?
Once you've divided out any common factors, the fraction that's left is irreducible.
4. it does say a possible divisor indicating the fraction could already be in its most reduced form
5. Thanks guys for helping me understand it

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Updated: July 13, 2009
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