Number Theory

Powers & Number Theory

Unlock divisibility checks, prime distribution, GCD/LCM, modular clocks, and exponential rules.

Lessons included in this chapter:

• Divisibility Rules: Each divisor has a shortcut: ÷3 checks digit sum, ÷4 checks last two digits, ÷9 checks digit sum again.
• Prime Factorisation: Divide by 2, then 3, then 5… until only 1 remains. Write the result as prime powers.
• GCD & LCM: GCD × LCM = a × b. For GCD: minimum prime powers. For LCM: maximum prime powers.
• Modular Arithmetic: a mod n is the remainder when a is divided by n. Once you reach n, wrap back to 0.
• Unit Digit of Powers: Unit digits of powers repeat in cycles of length 1, 2, or 4. Find the cycle, use remainder of exponent ÷ cycle length.