最大公因数计算器 — 公式

How to Find the Greatest Common Factor

Methods

Method 1: Prime Factorization 1. Find the prime factors of each number 2. Identify the common prime factors 3. Multiply the common factors together

Method 2: Euclidean Algorithm 1. Divide the larger number by the smaller 2. Replace the larger number with the remainder 3. Repeat until the remainder is 0 4. The last non-zero remainder is the GCF

Useful Identity

GCF(a, b) × LCM(a, b) = a × b

计算示例

Find the GCF of 48 and 36.

  1. Prime factorization of 48: 2⁴ × 3 = 2 × 2 × 2 × 2 × 3
  2. Prime factorization of 36: 2² × 3² = 2 × 2 × 3 × 3
  3. Common factors: 2² × 3 = 4 × 3
  4. GCF(48, 36) = 12