Final answer:
The greatest capacity of a bucket to empty the drums containing 50l, 60l, and 70l of oil with an exact number of fillings is 10 liters. This is found by calculating the Greatest Common Divisor (GCD) of the three quantities.
Step-by-step explanation:
The question is asking to find the greatest capacity of a bucket that can be used to empty three drums containing 50 liters, 60 liters, and 70 liters of oil respectively with an exact number of fillings. To solve this, we need to find the Greatest Common Divisor (GCD) of the three quantities. The GCD of 50, 60, and 70 is the largest number that divides all of them without leaving a remainder.
Let's find the GCD of these numbers:
- Factors of 50 are: 1, 2, 5, 10, 25, 50
- Factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Factors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70
The common factors are 1, 2, 5, and 10. Out of these, 10 is the greatest, so the greatest bucket capacity to empty each drum with an exact number of fillings is 10 liters.