Find the HCF of 24 and 36.

**The reasoning** HCF (Highest Common Factor) means the **largest number that divides both numbers exactly** without remainder. Let's find all factors: - **24:** 1, 2, 3, 4, 6, 8, **12**, 24 - **36:** 1, 2, 3, 4, 6, 9, **12**, 18, 36 The common factors are: 1, 2, 3, 4, 6, 12 The **highest** among them? **12** ✓ *Alternative method (prime factorization):* - 24 = 2³ × 3¹ - 36 = 2² × 3² HCF = take the **lowest power** of each common prime = 2² × 3¹ = 4 × 3 = **12** **Why the wrong options tempt you** **A) 6** — This IS a common factor, but not the *highest* one. Don't stop when you find one that works! **B) 8** — 8 divides 24, but check: does 36 ÷ 8 work? No! (36 ÷ 8 = 4.5). Always verify both numbers. **D) 72** — That's the LCM (Lowest Common Multiple), not HCF. Students often confuse these two concepts. **Quick takeaway** HCF is the **biggest** number that divides both—always smaller than or equal to the smallest number given (here, 24).