The remainder when \( 15^{963} \) is divided by 720 is \( 495 \).

Would you like further details on how this was calculated or have any other questions?

Here are 5 related questions you might explore:
1. What is the remainder when \( 12^{963} \) is divided by 720?
2. How does modular exponentiation work for large numbers?
3. Can you explain the Chinese Remainder Theorem for simplifying large modular arithmetic?
4. What is the remainder when \( 15^{1000} \) is divided by 720?
5. How do properties of divisibility help in remainder calculations?

**Tip:** Modular arithmetic helps simplify problems involving very large powers by reducing numbers modulo some divisor at each step.

Explore how to calculate the remainder of 15^963 divided by 720 using modular arithmetic and number theory principles. Learn key concepts such as modular exponentiation and the Chinese Remainder Theorem. Ideal for advanced math students.

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