1. Find the HCF of 12 and 18.
Difficulty: EasyType: MCQTopic: HCF and LCM
HCF or Highest Common Factor is the largest number that divides both numbers completely. We can find it using prime factorization or division method. Prime factorization: 12 equals 2 squared times 3. 18 equals 2 times 3 squared. HCF equals product of common prime factors with lowest powers equals 2 to the power 1 times 3 to the power 1 equals 6. Division method: Divide larger by smaller. 18 divided by 12 gives quotient 1 and remainder 6. Now divide 12 by 6 giving quotient 2 and remainder 0. So HCF equals 6.
Example code
// Method 1: Prime Factorization // 12 = 2² × 3 // 18 = 2 × 3² // HCF = 2¹ × 3¹ = 6 // Method 2: Euclidean Algorithm // HCF(18, 12): // 18 = 12 × 1 + 6 // 12 = 6 × 2 + 0 // HCF = 6 // Method 3: Division // Factors of 12: 1, 2, 3, 4, 6, 12 // Factors of 18: 1, 2, 3, 6, 9, 18 // Common: 1, 2, 3, 6 // Highest: 6