Prime Number: A number greater than 1 that has exactly two factors: 1 and itself
- Take each number in the list one by one
- Find all factors of that number
- Count the total number of factors
- If exactly 2 factors exist, circle it (it's prime)
- If more than 2 factors exist, leave it (it's composite)
Factors: 1, 13 → Prime (exactly 2 factors)
Factors: 1, 3, 5, 15 → Composite (4 factors)
Factors: 1, 17 → Prime (exactly 2 factors)
Factors: 1, 19 → Prime (exactly 2 factors)
Factors: 1, 3, 7, 21 → Composite (4 factors)
Factors: 1, 23 → Prime (exactly 2 factors)
Factors: 1, 5, 25 → Composite (3 factors)
Factors: 1, 3, 9, 27 → Composite (4 factors)
Factors: 1, 29 → Prime (exactly 2 factors)
Factors: 1, 31 → Prime (exactly 2 factors)
Circle: 13, 17, 19, 23, 29, 31
Leave uncircled: 15, 21, 25, 27
13 ÷ 1 = 13 remainder 0 → 1 is a factor
13 ÷ 2 = 6 remainder 1 → 2 is not a factor
13 ÷ 3 = 4 remainder 1 → 3 is not a factor
13 ÷ 4 = 3 remainder 1 → 4 is not a factor
13 ÷ 5 = 2 remainder 3 → 5 is not a factor
13 ÷ 6 = 2 remainder 1 → 6 is not a factor
13 ÷ 7 = 1 remainder 6 → 7 is not a factor
13 ÷ 8 = 1 remainder 5 → 8 is not a factor
13 ÷ 9 = 1 remainder 4 → 9 is not a factor
13 ÷ 10 = 1 remainder 3 → 10 is not a factor
13 ÷ 11 = 1 remainder 2 → 11 is not a factor
13 ÷ 12 = 1 remainder 1 → 12 is not a factor
13 ÷ 13 = 1 remainder 0 → 13 is a factor
The prime numbers in the list are: 13, 17, 19, 23, 29, and 31
• Prime Definition: Must have exactly two factors
• Factor Testing: Check divisibility systematically
• Counting: Only 2 factors means it's prime
Composite Number: A number greater than 1 that has more than two factors
Factors: 1, 2, 11, 22 → Composite (4 factors)
Factors: 1, 2, 3, 4, 6, 8, 12, 24 → Composite (8 factors)
Factors: 1, 2, 13, 26 → Composite (4 factors)
Factors: 1, 2, 4, 7, 14, 28 → Composite (6 factors)
Factors: 1, 2, 3, 5, 6, 10, 15, 30 → Composite (8 factors)
Factors: 1, 2, 4, 8, 16, 32 → Composite (6 factors)
Factors: 1, 3, 11, 33 → Composite (4 factors)
Factors: 1, 2, 17, 34 → Composite (4 factors)
Factors: 1, 5, 7, 35 → Composite (4 factors)
Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36 → Composite (9 factors)
Underline: 22, 24, 26, 28, 30, 32, 33, 34, 35, 36
All have more than 2 factors → all are composite
22 ÷ 1 = 22 remainder 0 → 1 is a factor
22 ÷ 2 = 11 remainder 0 → 2 is a factor
22 ÷ 3 = 7 remainder 1 → 3 is not a factor
22 ÷ 4 = 5 remainder 2 → 4 is not a factor
22 ÷ 5 = 4 remainder 2 → 5 is not a factor
22 ÷ 6 = 3 remainder 4 → 6 is not a factor
22 ÷ 7 = 3 remainder 1 → 7 is not a factor
22 ÷ 8 = 2 remainder 6 → 8 is not a factor
22 ÷ 9 = 2 remainder 4 → 9 is not a factor
22 ÷ 10 = 2 remainder 2 → 10 is not a factor
22 ÷ 11 = 2 remainder 0 → 11 is a factor
22 ÷ 12 = 1 remainder 10 → 12 is not a factor
22 ÷ 13 = 1 remainder 9 → 13 is not a factor
22 ÷ 14 = 1 remainder 8 → 14 is not a factor
22 ÷ 15 = 1 remainder 7 → 15 is not a factor
22 ÷ 16 = 1 remainder 6 → 16 is not a factor
22 ÷ 17 = 1 remainder 5 → 17 is not a factor
22 ÷ 18 = 1 remainder 4 → 18 is not a factor
22 ÷ 19 = 1 remainder 3 → 19 is not a factor
22 ÷ 20 = 1 remainder 2 → 20 is not a factor
22 ÷ 21 = 1 remainder 1 → 21 is not a factor
22 ÷ 22 = 1 remainder 0 → 22 is a factor
All numbers in the list are composite: 22, 24, 26, 28, 30, 32, 33, 34, 35, and 36
• Composite Definition: Must have more than two factors
• Factor Testing: Check divisibility systematically
• Counting: More than 2 factors means it's composite
Mixed classification: Determining if each number is prime or composite by finding its factors
Factors: 1, 37 → Prime (exactly 2 factors)
Factors: 1, 2, 19, 38 → Composite (4 factors)
Factors: 1, 3, 13, 39 → Composite (4 factors)
Factors: 1, 2, 4, 5, 8, 10, 20, 40 → Composite (8 factors)
Factors: 1, 41 → Prime (exactly 2 factors)
Factors: 1, 2, 3, 6, 7, 14, 21, 42 → Composite (8 factors)
Factors: 1, 43 → Prime (exactly 2 factors)
Factors: 1, 2, 4, 11, 22, 44 → Composite (6 factors)
Factors: 1, 3, 5, 9, 15, 45 → Composite (6 factors)
Factors: 1, 2, 23, 46 → Composite (4 factors)
37-P, 38-C, 39-C, 40-C, 41-P, 42-C, 43-P, 44-C, 45-C, 46-C
Primes: 37, 41, 43 | Composites: 38, 39, 40, 42, 44, 45, 46
Classification: 37-P, 38-C, 39-C, 40-C, 41-P, 42-C, 43-P, 44-C, 45-C, 46-C
• Systematic Analysis: Examine each number individually
• Factor Counting: Determine the exact number of factors
• Classification Rules: 2 factors = prime, more than 2 = composite
Prime Number: A number greater than 1 that has exactly two factors: 1 and itself
Composite Number: A number greater than 1 that has more than two factors
Factors: Numbers that divide evenly into another number without leaving a remainder
- Check if number > 1: Prime/composite only applies to numbers greater than 1
- Find all factors: Systematically check divisibility from 1 up to the number
- Count factors: Tally the total number of factors found
- Classify: 2 factors = prime, more than 2 = composite
• 1 is neither prime nor composite
• 2 is the smallest and only even prime number
• All primes greater than 2 are odd numbers
• The first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109...
• Every composite number has at least one prime factor
Word problems: Real-world situations requiring knowledge of factors and divisibility
Factors of 53: 1, 53
Option 1: Share with 1 student (53 ÷ 1 = 53 pencils each)
Option 2: Share with 53 students (53 ÷ 53 = 1 pencil each)
Since 53 has exactly 2 factors (1 and 53), it's prime
The teacher can share with 1 student (giving 53 pencils) or 53 students (giving 1 pencil each)
53 ÷ 1 = 53 remainder 0 → 1 is a factor
53 ÷ 2 = 26 remainder 1 → 2 is not a factor
53 ÷ 3 = 17 remainder 2 → 3 is not a factor
53 ÷ 4 = 13 remainder 1 → 4 is not a factor
53 ÷ 5 = 10 remainder 3 → 5 is not a factor
53 ÷ 6 = 8 remainder 5 → 6 is not a factor
53 ÷ 7 = 7 remainder 4 → 7 is not a factor
53 ÷ 8 = 6 remainder 5 → 8 is not a factor
53 ÷ 9 = 5 remainder 8 → 9 is not a factor
53 ÷ 10 = 5 remainder 3 → 10 is not a factor
53 ÷ 11 = 4 remainder 9 → 11 is not a factor
53 ÷ 12 = 4 remainder 5 → 12 is not a factor
53 ÷ 13 = 4 remainder 1 → 13 is not a factor
53 ÷ 14 = 3 remainder 11 → 14 is not a factor
53 ÷ 15 = 3 remainder 8 → 15 is not a factor
53 ÷ 16 = 3 remainder 5 → 16 is not a factor
53 ÷ 17 = 3 remainder 2 → 17 is not a factor
53 ÷ 18 = 2 remainder 17 → 18 is not a factor
53 ÷ 19 = 2 remainder 15 → 19 is not a factor
53 ÷ 20 = 2 remainder 13 → 20 is not a factor
53 ÷ 21 = 2 remainder 11 → 21 is not a factor
53 ÷ 22 = 2 remainder 9 → 22 is not a factor
53 ÷ 23 = 2 remainder 7 → 23 is not a factor
53 ÷ 24 = 2 remainder 5 → 24 is not a factor
53 ÷ 25 = 2 remainder 3 → 25 is not a factor
53 ÷ 26 = 2 remainder 1 → 26 is not a factor
53 ÷ 27 = 1 remainder 26 → 27 is not a factor
53 ÷ 28 = 1 remainder 25 → 28 is not a factor
53 ÷ 29 = 1 remainder 24 → 29 is not a factor
53 ÷ 30 = 1 remainder 23 → 30 is not a factor
53 ÷ 31 = 1 remainder 22 → 31 is not a factor
53 ÷ 32 = 1 remainder 21 → 32 is not a factor
53 ÷ 33 = 1 remainder 20 → 33 is not a factor
53 ÷ 34 = 1 remainder 19 → 34 is not a factor
53 ÷ 35 = 1 remainder 18 → 35 is not a factor
53 ÷ 36 = 1 remainder 17 → 36 is not a factor
53 ÷ 37 = 1 remainder 16 → 37 is not a factor
53 ÷ 38 = 1 remainder 15 → 38 is not a factor
53 ÷ 39 = 1 remainder 14 → 39 is not a factor
53 ÷ 40 = 1 remainder 13 → 40 is not a factor
53 ÷ 41 = 1 remainder 12 → 41 is not a factor
53 ÷ 42 = 1 remainder 11 → 42 is not a factor
53 ÷ 43 = 1 remainder 10 → 43 is not a factor
53 ÷ 44 = 1 remainder 9 → 44 is not a factor
53 ÷ 45 = 1 remainder 8 → 45 is not a factor
53 ÷ 46 = 1 remainder 7 → 46 is not a factor
53 ÷ 47 = 1 remainder 6 → 47 is not a factor
53 ÷ 48 = 1 remainder 5 → 48 is not a factor
53 ÷ 49 = 1 remainder 4 → 49 is not a factor
53 ÷ 50 = 1 remainder 3 → 50 is not a factor
53 ÷ 51 = 1 remainder 2 → 51 is not a factor
53 ÷ 52 = 1 remainder 1 → 52 is not a factor
53 ÷ 53 = 1 remainder 0 → 53 is a factor
The teacher can share her 53 pencils with 1 student (53 pencils each) or 53 students (1 pencil each). The number 53 is prime because it has exactly two factors: 1 and 53.
• Prime Application: Prime numbers have limited sharing options
• Real-world connection: Equal sharing requires understanding factors
• Verification: Confirm that sharing uses all pencils
Range analysis: Systematically checking numbers within a specified range
61, 62, 63, 64, 65, 66, 67, 68, 69
Factors: 1, 61 → prime
62 = 2 × 31 → composite
63 = 7 × 9 → composite
64 = 8 × 8 → composite
65 = 5 × 13 → composite
66 = 6 × 11 → composite
Factors: 1, 67 → prime
68 = 4 × 17 → composite
69 = 3 × 23 → composite
The prime numbers between 60 and 70 are: 61 and 67
• Systematic approach: Check each number in the range individually
• Even number rule: All even numbers > 2 are composite
• Verification: Double-check each classification
Prime Number Worksheet: Exercises focusing on identifying numbers with exactly two factors
Composite Number Worksheet: Exercises focusing on identifying numbers with more than two factors
Classification Worksheet: Activities that require distinguishing between prime and composite numbers
- Worksheet 1 (Prime): Take number 71 → factors are 1 and 71 → exactly 2 factors → prime
- Worksheet 2 (Composite): Take number 72 → factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 → 12 factors → composite
- Worksheet 3 (Pattern): Notice that all even numbers > 2 are composite
- Worksheet 4 (Application): Prime numbers limit how items can be arranged equally
• 2 is the only even prime number
• All primes > 2 are odd numbers
• Numbers ending in 5 (except 5) are composite
• Every number > 1 is either prime or composite
• Prime factorization is unique for each number