1. **State the problem:** We want to find what number divides the sum $4^{41} + 4^{42} + 4^{43}$ and check if it is divisible by 7. 2. **Rewrite the sum:** Factor out the smallest power of 4: $$4^{41} + 4^{42} + 4^{43} = 4^{41}(1 + 4 + 4^2)$$ 3. **Simplify inside the parentheses:** $$1 + 4 + 16 = 21$$ 4. **So the sum becomes:** $$4^{41} \times 21$$ 5. **Check divisibility by 7:** Since 21 is divisible by 7, the entire product is divisible by 7. 6. **Conclusion:** The sum $4^{41} + 4^{42} + 4^{43}$ is divisible by 7. **Final answer:** The sum is divisible by 7.