Find HCF of 24 and 36.

**The reasoning** HCF (Highest Common Factor) means the **largest number that divides both numbers completely** 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 Common factors: 1, 2, 3, 4, 6, 12 The **highest** one is **12**. *Quick check:* 24 ÷ 12 = 2 ✓ and 36 ÷ 12 = 3 ✓ **Why the wrong options tempt you** - **6** is a common factor, but not the *highest*. Don't stop searching too early! - **8** divides 24 perfectly, but doesn't divide 36 (36 ÷ 8 = 4.5). It's not even a common factor. - **72** is a common *multiple* (LCM), not a factor. The question asks what divides them, not what they both divide into. **Quick takeaway** HCF must divide **both** numbers completely, and you want the **biggest** one — list all common factors and pick the largest, or use prime factorization: 24 = 2³ × 3, 36 = 2² × 3², so HCF = 2² × 3 = 12.