[Verse 1]
Two numbers standing side by side
Seeking what they both divide
The greatest common thread they share
Euclid's method strips them bare
Take the larger, split by small
Watch the remainder as it falls
What's left behind becomes our guide
To the treasure tucked inside
[Chorus]
Divide and conquer, step by step
Until the remainder's zero's kept
The last divisor holds the key
GCD for you and me
Ancient wisdom, still so true
Euclidean magic pulling through
[Verse 2]
Two-fifty-two and one-oh-five
See the algorithm come alive
One-oh-five goes twice, leaves forty-two
Now the dance begins anew
Forty-two divides one-oh-five
Two times through with twenty-one alive
Twenty-one splits forty-two clean
Greatest common: twenty-one's the scene
[Chorus]
Divide and conquer, step by step
Until the remainder's zero's kept
The last divisor holds the key
GCD for you and me
Ancient wisdom, still so true
Euclidean magic pulling through
[Bridge]
Bézout whispers something more
Integers that unlock doors
X and Y exist to show
A times X plus B times Y's flow
Equals D, the common part
Extended algorithm's art
[Verse 3]
Three hundred years before our Lord
Euclid forged this mental sword
Logarithmic steps suffice
Efficiency beyond all price
From the larger to the small
'Til division conquers all
What remains when nothing's left
Is the prize of Euclid's theft
[Chorus]
Divide and conquer, step by step
Until the remainder's zero's kept
The last divisor holds the key
GCD for you and me
Ancient wisdom, still so true
Euclidean magic pulling through
[Outro]
Distillation's final call
Common essence conquers all