The HCF (Highest Common Factor) of 24 and 36 is the largest number that divides both 24 and 36 without leaving any remainder. This is a fundamental concept in arithmetic used in simplifying fractions, LCM calculations, and real-life problems.
The HCF is always less than or equal to both numbers. The LCM is always greater than or equal to both numbers. If HCF = 12 and LCM = 72, then 12 × 72 = 864 = 24 × 36 ✓
Step 1: Find the prime factors of each number.
24 = 2 × 12 = 2 × 2 × 6 = 2 × 2 × 2 × 3 = 2³ × 3¹
36 = 2 × 18 = 2 × 2 × 9 = 2 × 2 × 3 × 3 = 2² × 3²
Step 2: For HCF, take the lowest power of all common prime factors.
Common factors: 2 and 3
HCF = 4 × 3 = 12
Apply: a = bq + r
Step 1: 36 = 24 × 1 + 12 Step 2: 24 = 12 × 2 + 0 ← Remainder is 0!
Since remainder = 0, the divisor at this step is the HCF.
HCF (24, 36) = 12 ✓
Verification: 24 ÷ 12 = 2 ✓ and 36 ÷ 12 = 3 ✓
Bonus — LCM of 24 and 36: Using the relation: HCF × LCM = Product of two numbers 12 × LCM = 24 × 36 = 864 LCM = 864 ÷ 12 = 72
No, the HCF can never be greater than either of the given numbers. The HCF is at most equal to the smaller of the two numbers. If two numbers are coprime (no common factor except 1), their HCF is 1.
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