What is the capacity of the largest vessel which can empty the oil from three vessels containing 32 l, 24 l and 48 l an exact number of times?

Here's the continuation of your problems: 6. Find the largest size of handkerchiefs which can be cut from a cloth having length 2.75 m and breadth 75 cm. Step 1: Convert all measurements to the same unit. Convert meters to centimeters. 2.75 m = 2.75 × 100 cm = 275 cm The dimensions of the cloth are 275 cm by 75 cm. The largest size of square handkerchiefs will have a side length equal to the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) of the length and breadth. Step 2: Find the prime factorization of each dimension. 275 = 5 × 55 = 5 × 5 × 11 = 5^2 × 11 75 = 3 × 25 = 3 × 5 × 5 = 3 × 5^2 Step 3: Calculate the HCF by taking the lowest power of common prime factors. HCF(275, 75) = 5^2 = 25 The largest size of handkerchiefs is 25 cm. 7. What is the capacity of the largest vessel which can empty the oil from three vessels containing 32 L, 24 L and 48 L an exact number of times? Step 1: The capacity of the largest vessel must be a common divisor of 32 L, 24 L, and 48 L. We need to find the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) of these capacities. Step 2: Find the prime factorization of each capacity. 32 = 2^5 24 = 2^3 × 3 48 = 2^4 × 3 Step 3: Calculate the HCF by taking the lowest power of common prime factors. The common prime factor is 2. The lowest power of 2 among 2^5, 2^3, 2^4 is 2^3. The prime factor 3 is not common to all three numbers (it's missing in 32). HCF(32, 24, 48) = 2^3 = 8 The capacity of the largest vessel is 8 L. That's 2 down. 3 left today — send the next one.