Comments on: Python: Highest common factor of two numbers

By: st0le

st0le — Wed, 26 May 2010 10:36:48 +0000

The Binary GCD Algorithm is faster on a Computer…because a lot of its instructions are bit-shifts. So it is faster than Euclid’s on a Computer.

However, i’m not sure how python does it bit shift (maybe it uses multiply/divide by 2)

By: morlockhq

morlockhq — Tue, 08 Dec 2009 16:08:35 +0000

Now that you have the GCD of two numbers, you can use that for an efficient equation to calculate the Least Common Multiple (LCM) or two numbers.

LCM(a, b) = |a * b|/ GCD(a, b)

Math is nifty.

By: rouli

rouli — Tue, 08 Dec 2009 13:57:54 +0000

ah, it took me some time to understand how come the 145 in your example is not a multiply of 21, when both 252 and 105 are.
answer: it should be 147

By: mat

mat — Tue, 08 Dec 2009 13:55:55 +0000

@ Martin: I would have thought using subtraction would be quicker as modulo uses division however I tested it, and you are right!

@Juho: I did really want to implement it myself, as it’s good to learn the method and maths behind functions. Plus thanks for spotting my error, thats what I get for doing it by hand!

@Bojan: Thanks, I think Martin beat you to it though.

By: Bojan Resnik

Bojan Resnik — Tue, 08 Dec 2009 13:46:36 +0000

This is perhaps more commonly known as “greatest common divisor”, or gcd.
Euclid’s algorithm can be recursively defined as:

def gcd(a, b):
return a if b == 0 else gcd(b, a % b)

In your code, you are basically using subtraction to calculate a % b.

A bit more elegant iterative implementation in Python, using the modulo operator, would be:

def gcd(a, b):
while b:
a, b = b, a % b
return a

By: Juho Vepsäläinen

Juho Vepsäläinen — Tue, 08 Dec 2009 13:42:45 +0000

You can find gcd in the fractions module (http://docs.python.org/library/fractions.html#fractions.gcd). No need to implement one yourself unless you really want to.

By the way 252-105 equals 147, not 145.

By: Martin

Martin — Tue, 08 Dec 2009 13:41:09 +0000

It’s more efficient to use the modulo (%) operator:

def gcd(a,b):
while b: a, b = b, a%b
return a