Prime Number: A number greater than 1 that has exactly two factors: 1 and itself
- Start with 1 and check if it divides the number evenly
- Check 2, 3, 4, 5, up to the number itself
- List all numbers that divide evenly
- Count the total factors
- If exactly 2 factors exist, it's prime
107 ÷ 1 = 107 remainder 0 → 1 is a factor
107 ÷ 2 = 53 remainder 1 → 2 is not a factor
107 ÷ 3 = 35 remainder 2 → 3 is not a factor
107 ÷ 4 = 26 remainder 3 → 4 is not a factor
107 ÷ 5 = 21 remainder 2 → 5 is not a factor
107 ÷ 6 = 17 remainder 5 → 6 is not a factor
107 ÷ 7 = 15 remainder 2 → 7 is not a factor
107 ÷ 8 = 13 remainder 3 → 8 is not a factor
107 ÷ 9 = 11 remainder 8 → 9 is not a factor
107 ÷ 10 = 10 remainder 7 → 10 is not a factor
107 ÷ 11 = 9 remainder 8 → 11 is not a factor
107 ÷ 12 = 8 remainder 11 → 12 is not a factor
107 ÷ 13 = 8 remainder 3 → 13 is not a factor
107 ÷ 14 = 7 remainder 9 → 14 is not a factor
107 ÷ 15 = 7 remainder 2 → 15 is not a factor
107 ÷ 16 = 6 remainder 11 → 16 is not a factor
107 ÷ 17 = 6 remainder 5 → 17 is not a factor
107 ÷ 18 = 5 remainder 17 → 18 is not a factor
107 ÷ 19 = 5 remainder 12 → 19 is not a factor
107 ÷ 20 = 5 remainder 7 → 20 is not a factor
107 ÷ 21 = 5 remainder 2 → 21 is not a factor
107 ÷ 22 = 4 remainder 19 → 22 is not a factor
107 ÷ 23 = 4 remainder 15 → 23 is not a factor
107 ÷ 24 = 4 remainder 11 → 24 is not a factor
107 ÷ 25 = 4 remainder 7 → 25 is not a factor
107 ÷ 26 = 4 remainder 3 → 26 is not a factor
107 ÷ 27 = 3 remainder 26 → 27 is not a factor
107 ÷ 28 = 3 remainder 23 → 28 is not a factor
107 ÷ 29 = 3 remainder 20 → 29 is not a factor
107 ÷ 30 = 3 remainder 17 → 30 is not a factor
107 ÷ 31 = 3 remainder 14 → 31 is not a factor
107 ÷ 32 = 3 remainder 11 → 32 is not a factor
107 ÷ 33 = 3 remainder 8 → 33 is not a factor
107 ÷ 34 = 3 remainder 5 → 34 is not a factor
107 ÷ 35 = 3 remainder 2 → 35 is not a factor
107 ÷ 36 = 2 remainder 35 → 36 is not a factor
107 ÷ 37 = 2 remainder 33 → 37 is not a factor
107 ÷ 38 = 2 remainder 31 → 38 is not a factor
107 ÷ 39 = 2 remainder 29 → 39 is not a factor
107 ÷ 40 = 2 remainder 27 → 40 is not a factor
107 ÷ 41 = 2 remainder 25 → 41 is not a factor
107 ÷ 42 = 2 remainder 23 → 42 is not a factor
107 ÷ 43 = 2 remainder 21 → 43 is not a factor
107 ÷ 44 = 2 remainder 19 → 44 is not a factor
107 ÷ 45 = 2 remainder 17 → 45 is not a factor
107 ÷ 46 = 2 remainder 15 → 46 is not a factor
107 ÷ 47 = 2 remainder 13 → 47 is not a factor
107 ÷ 48 = 2 remainder 11 → 48 is not a factor
107 ÷ 49 = 2 remainder 9 → 49 is not a factor
107 ÷ 50 = 2 remainder 7 → 50 is not a factor
107 ÷ 51 = 2 remainder 5 → 51 is not a factor
107 ÷ 52 = 2 remainder 3 → 52 is not a factor
107 ÷ 53 = 2 remainder 1 → 53 is not a factor
107 ÷ 54 = 1 remainder 53 → 54 is not a factor
107 ÷ 55 = 1 remainder 52 → 55 is not a factor
107 ÷ 56 = 1 remainder 51 → 56 is not a factor
107 ÷ 57 = 1 remainder 50 → 57 is not a factor
107 ÷ 58 = 1 remainder 49 → 58 is not a factor
107 ÷ 59 = 1 remainder 48 → 59 is not a factor
107 ÷ 60 = 1 remainder 47 → 60 is not a factor
107 ÷ 61 = 1 remainder 46 → 61 is not a factor
107 ÷ 62 = 1 remainder 45 → 62 is not a factor
107 ÷ 63 = 1 remainder 44 → 63 is not a factor
107 ÷ 64 = 1 remainder 43 → 64 is not a factor
107 ÷ 65 = 1 remainder 42 → 65 is not a factor
107 ÷ 66 = 1 remainder 41 → 66 is not a factor
107 ÷ 67 = 1 remainder 40 → 67 is not a factor
107 ÷ 68 = 1 remainder 39 → 68 is not a factor
107 ÷ 69 = 1 remainder 38 → 69 is not a factor
107 ÷ 70 = 1 remainder 37 → 70 is not a factor
107 ÷ 71 = 1 remainder 36 → 71 is not a factor
107 ÷ 72 = 1 remainder 35 → 72 is not a factor
107 ÷ 73 = 1 remainder 34 → 73 is not a factor
107 ÷ 74 = 1 remainder 33 → 74 is not a factor
107 ÷ 75 = 1 remainder 32 → 75 is not a factor
107 ÷ 76 = 1 remainder 31 → 76 is not a factor
107 ÷ 77 = 1 remainder 30 → 77 is not a factor
107 ÷ 78 = 1 remainder 29 → 78 is not a factor
107 ÷ 79 = 1 remainder 28 → 79 is not a factor
107 ÷ 80 = 1 remainder 27 → 80 is not a factor
107 ÷ 81 = 1 remainder 26 → 81 is not a factor
107 ÷ 82 = 1 remainder 25 → 82 is not a factor
107 ÷ 83 = 1 remainder 24 → 83 is not a factor
107 ÷ 84 = 1 remainder 23 → 84 is not a factor
107 ÷ 85 = 1 remainder 22 → 85 is not a factor
107 ÷ 86 = 1 remainder 21 → 86 is not a factor
107 ÷ 87 = 1 remainder 20 → 87 is not a factor
107 ÷ 88 = 1 remainder 19 → 88 is not a factor
107 ÷ 89 = 1 remainder 18 → 89 is not a factor
107 ÷ 90 = 1 remainder 17 → 90 is not a factor
107 ÷ 91 = 1 remainder 16 → 91 is not a factor
107 ÷ 92 = 1 remainder 15 → 92 is not a factor
107 ÷ 93 = 1 remainder 14 → 93 is not a factor
107 ÷ 94 = 1 remainder 13 → 94 is not a factor
107 ÷ 95 = 1 remainder 12 → 95 is not a factor
107 ÷ 96 = 1 remainder 11 → 96 is not a factor
107 ÷ 97 = 1 remainder 10 → 97 is not a factor
107 ÷ 98 = 1 remainder 9 → 98 is not a factor
107 ÷ 99 = 1 remainder 8 → 99 is not a factor
107 ÷ 100 = 1 remainder 7 → 100 is not a factor
107 ÷ 101 = 1 remainder 6 → 101 is not a factor
107 ÷ 102 = 1 remainder 5 → 102 is not a factor
107 ÷ 103 = 1 remainder 4 → 103 is not a factor
107 ÷ 104 = 1 remainder 3 → 104 is not a factor
107 ÷ 105 = 1 remainder 2 → 105 is not a factor
107 ÷ 106 = 1 remainder 1 → 106 is not a factor
107 ÷ 107 = 1 remainder 0 → 107 is a factor
Yes, 107 is a prime number because it has exactly two factors: 1 and 107.
• 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
108 ÷ 1 = 108 remainder 0 → 1 is a factor
108 ÷ 2 = 54 remainder 0 → 2 is a factor
108 ÷ 3 = 36 remainder 0 → 3 is a factor
108 ÷ 4 = 27 remainder 0 → 4 is a factor
108 ÷ 5 = 21 remainder 3 → 5 is not a factor
108 ÷ 6 = 18 remainder 0 → 6 is a factor
108 ÷ 7 = 15 remainder 3 → 7 is not a factor
108 ÷ 8 = 13 remainder 4 → 8 is not a factor
108 ÷ 9 = 12 remainder 0 → 9 is a factor
108 ÷ 10 = 10 remainder 8 → 10 is not a factor
108 ÷ 11 = 9 remainder 9 → 11 is not a factor
108 ÷ 12 = 9 remainder 0 → 12 is a factor
108 ÷ 13 = 8 remainder 4 → 13 is not a factor
108 ÷ 14 = 7 remainder 10 → 14 is not a factor
108 ÷ 15 = 7 remainder 3 → 15 is not a factor
108 ÷ 16 = 6 remainder 12 → 16 is not a factor
108 ÷ 17 = 6 remainder 6 → 17 is not a factor
108 ÷ 18 = 6 remainder 0 → 18 is a factor
108 ÷ 19 = 5 remainder 13 → 19 is not a factor
108 ÷ 20 = 5 remainder 8 → 20 is not a factor
108 ÷ 21 = 5 remainder 3 → 21 is not a factor
108 ÷ 22 = 4 remainder 20 → 22 is not a factor
108 ÷ 23 = 4 remainder 16 → 23 is not a factor
108 ÷ 24 = 4 remainder 12 → 24 is not a factor
108 ÷ 25 = 4 remainder 8 → 25 is not a factor
108 ÷ 26 = 4 remainder 4 → 26 is not a factor
108 ÷ 27 = 4 remainder 0 → 27 is a factor
108 ÷ 28 = 3 remainder 24 → 28 is not a factor
108 ÷ 29 = 3 remainder 21 → 29 is not a factor
108 ÷ 30 = 3 remainder 18 → 30 is not a factor
108 ÷ 31 = 3 remainder 15 → 31 is not a factor
108 ÷ 32 = 3 remainder 12 → 32 is not a factor
108 ÷ 33 = 3 remainder 9 → 33 is not a factor
108 ÷ 34 = 3 remainder 6 → 34 is not a factor
108 ÷ 35 = 3 remainder 3 → 35 is not a factor
108 ÷ 36 = 3 remainder 0 → 36 is a factor
108 ÷ 37 = 2 remainder 34 → 37 is not a factor
108 ÷ 38 = 2 remainder 32 → 38 is not a factor
108 ÷ 39 = 2 remainder 30 → 39 is not a factor
108 ÷ 40 = 2 remainder 28 → 40 is not a factor
108 ÷ 41 = 2 remainder 26 → 41 is not a factor
108 ÷ 42 = 2 remainder 24 → 42 is not a factor
108 ÷ 43 = 2 remainder 22 → 43 is not a factor
108 ÷ 44 = 2 remainder 20 → 44 is not a factor
108 ÷ 45 = 2 remainder 18 → 45 is not a factor
108 ÷ 46 = 2 remainder 16 → 46 is not a factor
108 ÷ 47 = 2 remainder 14 → 47 is not a factor
108 ÷ 48 = 2 remainder 12 → 48 is not a factor
108 ÷ 49 = 2 remainder 10 → 49 is not a factor
108 ÷ 50 = 2 remainder 8 → 50 is not a factor
108 ÷ 51 = 2 remainder 6 → 51 is not a factor
108 ÷ 52 = 2 remainder 4 → 52 is not a factor
108 ÷ 53 = 2 remainder 2 → 53 is not a factor
108 ÷ 54 = 2 remainder 0 → 54 is a factor
108 ÷ 55 = 1 remainder 53 → 55 is not a factor
108 ÷ 56 = 1 remainder 52 → 56 is not a factor
108 ÷ 57 = 1 remainder 51 → 57 is not a factor
108 ÷ 58 = 1 remainder 50 → 58 is not a factor
108 ÷ 59 = 1 remainder 49 → 59 is not a factor
108 ÷ 60 = 1 remainder 48 → 60 is not a factor
108 ÷ 61 = 1 remainder 47 → 61 is not a factor
108 ÷ 62 = 1 remainder 46 → 62 is not a factor
108 ÷ 63 = 1 remainder 45 → 63 is not a factor
108 ÷ 64 = 1 remainder 44 → 64 is not a factor
108 ÷ 65 = 1 remainder 43 → 65 is not a factor
108 ÷ 66 = 1 remainder 42 → 66 is not a factor
108 ÷ 67 = 1 remainder 41 → 67 is not a factor
108 ÷ 68 = 1 remainder 40 → 68 is not a factor
108 ÷ 69 = 1 remainder 39 → 69 is not a factor
108 ÷ 70 = 1 remainder 38 → 70 is not a factor
108 ÷ 71 = 1 remainder 37 → 71 is not a factor
108 ÷ 72 = 1 remainder 36 → 72 is not a factor
108 ÷ 73 = 1 remainder 35 → 73 is not a factor
108 ÷ 74 = 1 remainder 34 → 74 is not a factor
108 ÷ 75 = 1 remainder 33 → 75 is not a factor
108 ÷ 76 = 1 remainder 32 → 76 is not a factor
108 ÷ 77 = 1 remainder 31 → 77 is not a factor
108 ÷ 78 = 1 remainder 30 → 78 is not a factor
108 ÷ 79 = 1 remainder 29 → 79 is not a factor
108 ÷ 80 = 1 remainder 28 → 80 is not a factor
108 ÷ 81 = 1 remainder 27 → 81 is not a factor
108 ÷ 82 = 1 remainder 26 → 82 is not a factor
108 ÷ 83 = 1 remainder 25 → 83 is not a factor
108 ÷ 84 = 1 remainder 24 → 84 is not a factor
108 ÷ 85 = 1 remainder 23 → 85 is not a factor
108 ÷ 86 = 1 remainder 22 → 86 is not a factor
108 ÷ 87 = 1 remainder 21 → 87 is not a factor
108 ÷ 88 = 1 remainder 20 → 88 is not a factor
108 ÷ 89 = 1 remainder 19 → 89 is not a factor
108 ÷ 90 = 1 remainder 18 → 90 is not a factor
108 ÷ 91 = 1 remainder 17 → 91 is not a factor
108 ÷ 92 = 1 remainder 16 → 92 is not a factor
108 ÷ 93 = 1 remainder 15 → 93 is not a factor
108 ÷ 94 = 1 remainder 14 → 94 is not a factor
108 ÷ 95 = 1 remainder 13 → 95 is not a factor
108 ÷ 96 = 1 remainder 12 → 96 is not a factor
108 ÷ 97 = 1 remainder 11 → 97 is not a factor
108 ÷ 98 = 1 remainder 10 → 98 is not a factor
108 ÷ 99 = 1 remainder 9 → 99 is not a factor
108 ÷ 100 = 1 remainder 8 → 100 is not a factor
108 ÷ 101 = 1 remainder 7 → 101 is not a factor
108 ÷ 102 = 1 remainder 6 → 102 is not a factor
108 ÷ 103 = 1 remainder 5 → 103 is not a factor
108 ÷ 104 = 1 remainder 4 → 104 is not a factor
108 ÷ 105 = 1 remainder 3 → 105 is not a factor
108 ÷ 106 = 1 remainder 2 → 106 is not a factor
108 ÷ 107 = 1 remainder 1 → 107 is not a factor
108 ÷ 108 = 1 remainder 0 → 108 is a factor
Yes, 108 is a composite number because it has more than two factors: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
• Composite Definition: Must have more than two factors
• Factor Pairs: 1×108=108, 2×54=108, 3×36=108, 4×27=108, 6×18=108, 9×12=108
• Counting: More than 2 factors means it's composite
Classification: Determining if each number is prime or composite by finding its factors
Factors: 1, 101 → Prime (exactly 2 factors)
Factors: 1, 103 → Prime (exactly 2 factors)
Factors: 1, 3, 5, 7, 15, 21, 35, 105 → Composite (8 factors)
Factors: 1, 107 → Prime (exactly 2 factors)
Factors: 1, 109 → Prime (exactly 2 factors)
Prime: 101, 103, 107, 109 | Composite: 105
Prime numbers: 101, 103, 107, 109 | Composite number: 105
• 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 113: 1, 113
Option 1: 1 row of 113 marbles (1×113)
Option 2: 113 rows of 1 marble each (113×1)
Since 113 has exactly 2 factors (1 and 113), it's prime
Sarah can arrange the marbles in only 2 ways: 1 row of 113 marbles or 113 rows of 1 marble each
Sarah can arrange her 113 marbles in 1 row of 113 marbles or 113 rows of 1 marble each. The number 113 is prime because it has exactly two factors: 1 and 113.
• Prime Application: Prime numbers have limited arrangement options
• Real-world connection: Arranging objects requires understanding factors
• Verification: Confirm that arrangements use all marbles
Range analysis: Systematically checking numbers within a specified range
111, 112, 113, 114, 115, 116, 117, 118, 119
111 = 3 × 37 → composite
112 = 16 × 7 → composite
Factors: 1, 113 → prime
114 = 6 × 19 → composite
115 = 5 × 23 → composite
116 = 4 × 29 → composite
117 = 9 × 13 → composite
118 = 2 × 59 → composite
119 = 7 × 17 → composite
The prime number between 110 and 120 is: 113
• 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 Test: Exercises focusing on identifying numbers with exactly two factors
Composite Number Test: Problems focusing on identifying numbers with more than two factors
Classification Test: Activities that require distinguishing between prime and composite numbers
- Test 1 (Prime): Take number 109 → factors are 1 and 109 → exactly 2 factors → prime
- Test 2 (Composite): Take number 110 → factors are 1, 2, 5, 10, 11, 22, 55, 110 → 8 factors → composite
- Test 3 (Pattern): Notice that all even numbers > 2 are composite
- Test 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