A farmer harvested 100kg of millet and 56kg of maize. He wants to pour them into containers of equal mass. What is the greatest mass of a container he can have?

Question 1

Answer · 2026-03-18T12:20:43.067Z

Step 1: Identify the masses of the three containers of maize from the two farmers and the miller. Masses: 100 kg, 150 kg, 200 kg. The greatest mass m kg per new container must divide each original mass exactly (using all maize from each without mixing sources). Thus, m = (100, 150, 200). Step 2: Compute (100, 150) using Euclidean algorithm. 150 = 1 × 100 + 50 100 = 2 × 50 + 0 So, (100, 150) = 50 kg. Step 3: Now compute (50, 200). 200 = 4 × 50 + 0 So, (50, 200) = 50 kg. Step 4: Verify 50 kg divides each mass. 100 ÷ 50 = 2 containers 150 ÷ 50 = 3 containers 200 ÷ 50 = 4 containers All integers, uses all maize. No larger common divisor exists. The greatest mass of maize per container is 50 kg.

Question 2

Step 1: Identify the masses of the three containers of maize from the two farmers and the miller. Masses: 100 kg, 150 kg, 200 kg. The greatest mass m kg per new container must divide each original mass exactly (using all maize from each without mixing sources). Thus, m = (100, 150, 200). Step 2: Compute (100, 150) using Euclidean algorithm. 150 = 1 × 100 + 50 100 = 2 × 50 + 0 So, (100, 150) = 50 kg. Step 3: Now compute (50, 200). 200 = 4 × 50 + 0 So, (50, 200) = 50 kg. Step 4: Verify 50 kg divides each mass. 100 ÷ 50 = 2 containers 150 ÷ 50 = 3 containers 200 ÷ 50 = 4 containers All integers, uses all maize. No larger common divisor exists. The greatest mass of maize per container is 50 kg.

A farmer harvested 100kg of millet and 56kg of maize. He wants to pour them into containers of equal mass. What is the greatest mass of a container he can have?

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