Estimate the following numbers to the nearest thousand and find their difference.

The thousands digit is 3. The digit to its right is 7. Since $7 \ge 5$, we round up the thousands digit.

$$13,782 \approx 14,000$$

The thousands digit is 1. The digit to its right is 6. Since $6 \ge 5$, we round up the thousands digit.

$$11,642 \approx 12,000$$

$$14,000 - 12,000 = 2,000$$

The difference is $\boxed{2,000}$.

2.

The thousands digit is 9. The digit to its right is 5. Since $5 \ge 5$, we round up the thousands digit. This changes the 79 to 80.

$$79,582 \approx 80,000$$

The thousands digit is 6. The digit to its right is 4. Since $4 < 5$, we keep the thousands digit as it is.

$$66,442 \approx 66,000$$

$$80,000 - 66,000 = 14,000$$

The difference is $\boxed{14,000}$.

3.

The thousands digit is 0. The digit to its right is 3. Since $3 < 5$, we keep the thousands digit as it is.

$$870,345 \approx 870,000$$

The thousands digit is 9. The digit to its right is 8. Since $8 \ge 5$, we round up the thousands digit. This changes the 459 to 460.

$$459,876 \approx 460,000$$

$$870,000 - 460,000 = 410,000$$

The difference is $\boxed{410,000}$.