Fill in the blanks so that the equality holds
`589xx365=365xx________`

Answer

To solve the equation \( 589 \times 365 = 365 \times \_\_\_\_\_ \), we need to find the number that can replace the blank so that both sides of the equation are equal.

### Step-by-step Solution:

1. **Understand the Equality**: The equation states that \( 589 \times 365 \) is equal to \( 365 \times \_\_\_\_\_ \). This means that whatever we multiply 365 by on the right side must equal \( 589 \) when multiplied by 365 on the left side.

2. **Use the Commutative Property of Multiplication**: The commutative property of multiplication tells us that the order in which we multiply numbers does not change the product. This means:
\[ a \times b = b \times a \]
So, we can rewrite the left side:
\[ 589 \times 365 = 365 \times 589 \]

3. **Fill in the Blank**: Since we have established that \( 589 \times 365 = 365 \times 589 \), we can see that the blank should be filled with \( 589 \):
\[ 589 \times 365 = 365 \times 589 \]

4. **Final Answer**: Therefore, the number that fills the blank is:
\[ 589 \]

### Final Statement:
The completed equation is:
\[ 589 \times 365 = 365 \times 589 \]