The Euclidean algorithm https://en.wikipedia.org/wiki/Euclidean_algorithm is an efficient method of finding the GCD (greatest common divisor) of two integers. It proceeds by finding successive remainders of the larger by the smaller and swapping the smaller with the remainder until the remainder equals zero, returning the divisor as the GCD.

The code was developed on an HP16C emulator and so works on the DM16 but will run on any DM calculator.

Line 4 LBL E for Euclid is the normal entry point after entering your two numbers, i.e. <number 1> ENTER <number 2> GSB E, the GCD is returned. The re-entrant loop at line 1 LBL F is only for non-zero remainders. Only stack variables x, y and LST X are used and no Registers.

## [DM16] Euclidean algorithm in stack

### Re: [DM16] Euclidean algorithm in stack

You can do it with just LBL E:
Cheers, Werner

Code: Select all

```
LBL E
RMD
LASTX
X<>Y
X!=0?
GTO E
+
RTN
```

42S #3249S01123

DM42 #00345

DM42 #00345

### Re: [DM16] Euclidean algorithm in stack

thanks you are correct. The DM16 code was intended to illustrate what was possible using the stack rather than optimal. thanks again Iain