Greatest Common Divisor
- Tags
- math
Is a concept describing the largest factor shared by two non-zero numbers \( x, y \), written as \( \gcd (x, y) \).
Table 1:
Listing of the unique divisors of both 8 and 12. \label{tbl:gcd-8-12-eg}
| Number | Factor Pairs | Unique Divisors |
|---|---|---|
| 8 | \( 8 \times 1 \), \( 4 \times 2 \) | 1, 2, 4, 8 |
| 12 | \( 12 \times 1 \), \( 6 \times 2 \), \( 3 \times 4 \) | 1, 2, 3, 4, 6, 8 |
For example consider \( \gcd (8, 12) \). From tbl:gcd-8-12-eg it can be shown that they both share the factors 1, 2 and 4. The largest of these is 4 therefore \( \gcd (8, 12) = 4 \).