2. A winemaker has three kinds of wine. He has 400 litres of chenin blane, 440 litres chardonnay and 460 litres of sauvignon blanc. Calculate the smallest possible number of barrels with equal volumes which can be fillec with the different wines without mixing them so that no wine is left.

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To determine the smallest possible number of barrels with equal volumes that can be used to store the different types of wine without any leftovers, we need to find the **greatest common divisor (GCD)** of the volumes of the three wines. This GCD will represent the largest possible barrel volume that can exactly divide each type of wine without leaving any remainder.

### Step-by-Step Solution:

1. **Identify the Volumes:**
   - **Chenin Blanc:** 400 litres
   - **Chardonnay:** 440 litres
   - **Sauvignon Blanc:** 460 litres

2. **Find the GCD of the Three Volumes:**

- **GCD of 400 and 440:**
     - $$ 440 - 400 = 40 $$
     - $$ 	ext{GCD}(400, 40) = 40 $$
   
   - **GCD of 40 and 460:**
     - $$ 460 - 40 	imes 11 = 20 $$
     - $$ 	ext{GCD}(40, 20) = 20 $$

- **Final GCD:** 20 litres

3. **Determine the Number of Barrels Needed for Each Wine Type:**
   
   - **Chenin Blanc:**
     - $$ \frac{400 	ext{ litres}}{20 	ext{ litres/barrel}} = 20 	ext{ barrels} $$
   
   - **Chardonnay:**
     - $$ \frac{440 	ext{ litres}}{20 	ext{ litres/barrel}} = 22 	ext{ barrels} $$
   
   - **Sauvignon Blanc:**
     - $$ \frac{460 	ext{ litres}}{20 	ext{ litres/barrel}} = 23 	ext{ barrels} $$

4. **Calculate the Total Number of Barrels:**
   - $$ 20 	ext{ barrels} + 22 	ext{ barrels} + 23 	ext{ barrels} = 65 	ext{ barrels} $$

### Conclusion:

The smallest possible number of barrels, each with a volume of **20 litres**, required to store all the wines without any leftovers is **65 barrels**.

**Answer:** 65 barrels are needed when each barrel holds 20 litres.
To store all the wines without leftovers, each barrel must hold 20 litres. Therefore, the winemaker needs a total of 65 barrels. **Answer:** 65 barrels are needed.

A winemaker has three kinds of wine. He has 400 litres of chenin blane,
440 litres chardonnay and 460 litres of sauvignon blanc. Calculate the
smallest possible number of barrels with equal volumes which can be fillec
with the different wines without mixing them so that no wine is left.

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