Number Theory

Primes, divisibility, GCF, LCM and modular arithmetic

Explore the mathematical properties of integers — prime numbers, factors, multiples and modular arithmetic.

✓ Prime: exactly 2 factors (1 and itself)✓ Every integer has unique prime factoriza...✓ GCF: largest common factor

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📖 Understanding Number Theory

A prime number is a natural number greater than 1 with exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13... The fundamental theorem of arithmetic states every integer > 1 has a unique prime factorization.

GCF (Greatest Common Factor): the largest number that divides both. Find using prime factorization or Euclidean algorithm. LCM (Least Common Multiple): the smallest number divisible by both. LCM × GCF = product of the two numbers.

Divisibility rules: A number is divisible by 2 if it ends in an even digit; by 3 if digit sum is divisible by 3; by 5 if it ends in 0 or 5; by 9 if digit sum is divisible by 9.

Modular arithmetic (clock arithmetic): a ≡ b (mod n) means a and b leave the same remainder when divided by n. Used in cryptography, computer science and competition maths.

🔑 Key Points to Remember

✓Prime: exactly 2 factors (1 and itself)
✓Every integer has unique prime factorization
✓GCF: largest common factor
✓LCM: smallest common multiple
✓LCM × GCF = product of two numbers

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🔗 Related Topics

🔤Introduction to Algebra ½Fractions