Calculate the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of multiple numbers. See prime factorizations and step-by-step solutions.
GCF
12
Greatest Common Factor
Step 1: Find prime factorizations
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
Step 2: Find common prime factors
Common factors: 1, 2, 3, 4, 6, 12
Step 3: Multiply common factors
GCF = 2 × 2 × 3 = 12
GCF(24, 36) = 12
Factors of 24:
1, 2, 3, 4, 6, 8, 12, 24
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
Highlighted numbers are common factors
For two numbers: GCF × LCM = Product
12 × 72 = 864 = 24 × 36 ✓
Check GCF divides all numbers:
24 ÷ 12 = 2 ✓
36 ÷ 12 = 3 ✓
Check LCM divisible by all:
72 ÷ 24 = 3 ✓
72 ÷ 36 = 2 ✓
Test your understanding with real problems
Practice with 6 problems to test your understanding.
GCF
12
Greatest Common Factor
The Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD), is the largest number that divides evenly into all given numbers. To find the GCF: list prime factors of each number, identify common factors, and multiply them together. For example, GCF(12, 18) = 6, because 6 is the largest number that divides both 12 and 18 evenly.
The Greatest Common Factor (GCF), also known as Greatest Common Divisor (GCD) or Highest Common Factor (HCF), is the largest positive integer that divides two or more integers without leaving a remainder. It is fundamental in simplifying fractions, finding equivalent ratios, and solving problems involving divisibility.
The Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD), is the largest number that divides evenly into all given numbers. To find the GCF: list prime factors of each number, identify common factors, and multiply them together. For example, GCF(12, 18) = 6, because 6 is the largest number that divides both 12 and 18 evenly.
The GCF (also called GCD - Greatest Common Divisor) is the largest number that divides evenly into all given numbers. For example, the GCF of 12 and 18 is 6 because 6 is the largest number that divides both 12 and 18 without a remainder.
The LCM is the smallest positive number that is a multiple of all given numbers. For example, the LCM of 4 and 6 is 12 because 12 is the smallest number that both 4 and 6 divide into evenly.
List the prime factorization of each number. Find all prime factors that appear in ALL factorizations. Multiply these common factors together. Example: 12 = 2² × 3, 18 = 2 × 3². Common factors: 2 × 3 = 6.
List the prime factorization of each number. Take each prime factor at its highest power that appears. Multiply them together. Example: 12 = 2² × 3, 18 = 2 × 3². LCM = 2² × 3² = 36.
For any two numbers a and b: GCF(a, b) × LCM(a, b) = a × b. This relationship helps verify calculations. Example: GCF(12, 18) = 6, LCM(12, 18) = 36. Check: 6 × 36 = 216 = 12 × 18 ✓
Last updated: 2025-01-15
GCF
12
Greatest Common Factor