Identify prime and composite numbers, understand their properties, and use prime factorization to break down numbers
A prime number has exactly two factors: 1 and itself. A composite number has more than two factors. 1 is neither prime nor composite.
Prime numbers are the building blocks of all integers, essential for understanding number theory and advanced mathematics.
Prime numbers form the foundation of modern computer security and encryption systems used in digital communications.
Prime factorization provides systematic methods for solving fraction, ratio, and proportion problems efficiently.
Step 1: Test divisibility by primes up to √17 ≈ 4.1
Step 2: Test: 17 ÷ 2 = 8.5 (not divisible), 17 ÷ 3 = 5.67 (not divisible)
Answer: 17 is prime - it only has factors 1 and 17
Factor Tree: 60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5
Answer: 60 = 2² × 3 × 5
Check: 2² × 3 × 5 = 4 × 3 × 5 = 60 ✓
Test each number:
11: Only factors 1, 11 → Prime
13: Only factors 1, 13 → Prime
17: Only factors 1, 17 → Prime
19: Only factors 1, 19 → Prime
Answer: 4 prime numbers (11, 13, 17, 19)
Learn from typical errors students make and discover how to avoid them!
What students often do wrong:
Students often think 1 is a prime number, confuse the definitions of prime and composite, or make incomplete factor trees by stopping before reaching all prime factors.
Correct approach: Remember: 1 is neither prime nor composite. Prime numbers have exactly two factors (1 and themselves). Keep factoring until all branches end in prime numbers.
Memory tip: "Prime has precisely two factors" - use this phrase to remember the definition.
Practice the divisibility rules for 2, 3, 5, and 7 to quickly identify composite numbers. Remember that only testing up to the square root of a number is sufficient for prime testing.
You've mastered Prime and Composite Numbers!
Next: Master calculator skills and verify your mental calculations