Shortcut Trick Identify the difference between the two numbers: 144 − 108 = 36. The HCF must be a factor of this difference. Check if 36 divides both: 108 ÷ 36 = 3 and 144 ÷ 36 = 4. Since 36 is the highest common divisor, it is the HCF. ∴ The correct answer is 36. Alternate Method Given: Numbers are 108 and 144. Method: Prime Factorization ⇒ Prime factors of 108 = 2 × 2 × 3 × 3 × 3 = 2^(2) × 3^(3) ⇒ Prime factors of 144 = 2 × 2 × 2 × 2 × 3 × 3 = 2^(4) × 3^(2) ⇒ HCF = Product of the lowest powers of common prime factors ⇒ HCF = 2^(2) × 3^(2) ⇒ HCF = 4 × 9 = 36 ∴ The correct answer is 36. Related Concepts: Highest Common Factor (HCF) The HCF (or GCD) is the largest positive integer that divides each of the integers without a remainder. Relationship between HCF and LCM For two numbers a and b: HCF(a, b) × LCM(a, b) = a × b. Division Method for HCF Divide the larger number by the smaller, then divide the divisor by the remainder until the remainder is zero; the last divisor is the HCF.