Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.Deselect Answer 200 Kg 290 Kg 350 Kg 98 Kg
Question
Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.Deselect Answer 200 Kg 290 Kg 350 Kg 98 Kg
Solution
To find the maximum capacity of a bag so that the wheat can be packed in exact number of bags, we need to find the greatest common divisor (GCD) of the weights of the wheat that the farmers have.
The weights of the wheat are 490 kg, 588 kg, and 882 kg. To find the GCD, we can use the Euclidean algorithm.
Step 1: Find the GCD of 490 kg and 588 kg.
- Divide 588 kg by 490 kg: 588 kg ÷ 490 kg = 1 with a remainder of 98 kg.
- Replace 588 kg with 490 kg and 490 kg with the remainder, 98 kg.
- Repeat the division: 490 kg ÷ 98 kg = 5 with a remainder of 0 kg.
- The GCD of 490 kg and 588 kg is 98 kg.
Step 2: Find the GCD of 98 kg and 882 kg.
- Divide 882 kg by 98 kg: 882 kg ÷ 98 kg = 9 with a remainder of 0 kg.
- The GCD of 98 kg and 882 kg is 98 kg.
Therefore, the maximum capacity of a bag that can be used to pack the wheat in exact number of bags is 98 kg.
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