Factors, Multiples, and Primes
Prime number: Exactly two factors — 1 and itself. First primes: 2, 3, 5, 7, 11, 13, 17, 19, 23... (2 is the only even prime.)
Composite number: More than two factors.
Prime factorization: Express as a product of primes. 60 = 2² × 3 × 5.
GCF (Greatest Common Factor): Largest factor shared by two numbers. Use prime factorization: multiply all shared primes at their lowest powers. GCF(12, 18): 12 = 2²×3, 18 = 2×3² → GCF = 2×3 = 6.
LCM (Least Common Multiple): Smallest number divisible by both. Use prime factorization: take each prime at its highest power. LCM(4, 6): 4 = 2², 6 = 2×3 → LCM = 2²×3 = 12.
Divisibility rules: - By 2: last digit even · By 3: digit sum divisible by 3 · By 4: last two digits divisible by 4 · By 5: ends in 0 or 5 · By 9: digit sum divisible by 9 · By 10: ends in 0