Format Fraction on picker to lowest common denominator? - iphone

Question

Below is how I am formatting my picker currently. I would really like it to show 1/8 instead of 2/16 or 1/2 instead of 8/16. How can I adjust this to show my desired output? Thank you!
fractionArray = [[NSMutableArray alloc] init];
for(int frac = 0; frac <= 15; frac ++){
NSString *fracString = [NSString stringWithFormat:#"%d/16", frac];
[fractionArray addObject:fracString]; // Add the string.

Answer 1

Kids these days... Euclidean algorithm... what are they teaching in school... grumble grumble...
int gcd(int a, int b) {
// assumes a >= 0 && b > 0
while (b != 0) {
int t = a % b;
a = b;
b = t;
}
return a;
}
NSString *stringByReducingFraction(int a, int b) {
if (a == 0) return #"0";
if (a == b) return #"1";
int g = gcd(a, b);
return [NSString stringWithFormat:#"%d/%d", a / g, b / g];
}

Answer 2

This should work for any power of 2 denominator:
// dodge this special case:
[fractionArray addObject:#"0"];
for ( int numerator = 1; numerator <= 15; numerator++ )
{
int denominator = 16;
int num = numerator;
while ( num % 2 == 0 )
{
num /= 2;
denominator /= 2;
}
NSString *fracString = [NSString stringWithFormat:#"%d/%d", num, denominator];
[fractionArray addObject:fracString]; // Add the string.
}
And it's easy to extend this to any denominator. (Hint: replace 2 with n, iterate n from 2 up to sqrt(denominator).)
EDIT: actually works now!
Since I went ahead and coded it, here's the version that factors any denominator:
int denominator = 240;
for ( int numerator = 1; numerator < denominator; numerator++ )
{
int denom = denominator;
int num = numerator;
int factor = 2;
while ( factor * factor < denom )
{
while ( (num % factor) == 0 && (denom % factor) == 0 )
{
num /= factor;
denom /= factor;
}
// don't worry about finding the next prime,
// the loop above will skip composites
++factor;
}
NSString *fracString = [NSString stringWithFormat:#"%d/%d", num, denom];
[fractionArray addObject:fracString];
}