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We want the GCD of 9741: 3 * 17 * 191. In order to get that...
9741 is divisible by 3 and equal to 3247 * 3 therefore we have 3 * 3247.
3247 is divisible by 17 and equal to 191 * 17 therefore we have 3 * 17 * 191, these are all prime numbers so no more factorization for this part.
Now we need to prime factorize the 221.
221 is divisible by 13 and equal to 17 * 13 therefore we have 13 * 17 which are all prime numbers meaning no more factorization.
Now we want to factor out 17 from the numerator/denominator
9741 = 17 * 573
221 = 17 * 13
In other words...(Same thing cancel the common factor of 17)
9741 is divisible by 3 and equal to 3247 * 3 therefore we have 3 * 3247.
3247 is divisible by 17 and equal to 191 * 17 therefore we have 3 * 17 * 191, these are all prime numbers so no more factorization for this part.
Now we need to prime factorize the 221.
221 is divisible by 13 and equal to 17 * 13 therefore we have 13 * 17 which are all prime numbers meaning no more factorization.
Now we want to factor out 17 from the numerator/denominator
9741 = 17 * 573
221 = 17 * 13
In other words...(Same thing cancel the common factor of 17)