Greatest Common Divisor (GCD)
The Greatest Common Divisor is the largest number that divides two or more numbers exactly, with no remainder!
What is a Common Divisor?
A common divisor is a number that divides two or more numbers exactly (with no remainder).
Example: Is 4 a common divisor of 12 and 20?
- 12 ÷ 4 = 3 ✓ (exact division)
- 20 ÷ 4 = 5 ✓ (exact division)
Yes! 4 is a common divisor of 12 and 20.
Finding Common Divisors
Steps to find common divisors:
- List ALL divisors of the first number
- List ALL divisors of the second number
- Find numbers that appear in BOTH lists
| Divisors of 12: | 1, 2, 3, 4, 6, 12 |
|---|---|
| Divisors of 18: | 1, 2, 3, 6, 9, 18 |
| Common divisors: | 1, 2, 3, 6 |
The Greatest Common Divisor (GCD)
The Greatest Common Divisor (GCD) is the largest of all common divisors.
Other names for GCD:
- GCF - Greatest Common Factor
- HCF - Highest Common Factor
- НОД - Наибольший Общий Делитель (Russian)
Notation: GCD(12, 18) = 6
Interactive visualization — available in the full lesson