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
83 ÷ 1 = 83 remainder 0 → 1 is a factor
83 ÷ 2 = 41 remainder 1 → 2 is not a factor
83 ÷ 3 = 27 remainder 2 → 3 is not a factor
83 ÷ 4 = 20 remainder 3 → 4 is not a factor
83 ÷ 5 = 16 remainder 3 → 5 is not a factor
83 ÷ 6 = 13 remainder 5 → 6 is not a factor
83 ÷ 7 = 11 remainder 6 → 7 is not a factor
83 ÷ 8 = 10 remainder 3 → 8 is not a factor
83 ÷ 9 = 9 remainder 2 → 9 is not a factor
83 ÷ 10 = 8 remainder 3 → 10 is not a factor
83 ÷ 11 = 7 remainder 6 → 11 is not a factor
83 ÷ 12 = 6 remainder 11 → 12 is not a factor
83 ÷ 13 = 6 remainder 5 → 13 is not a factor
83 ÷ 14 = 5 remainder 13 → 14 is not a factor
83 ÷ 15 = 5 remainder 8 → 15 is not a factor
83 ÷ 16 = 5 remainder 3 → 16 is not a factor
83 ÷ 17 = 4 remainder 15 → 17 is not a factor
83 ÷ 18 = 4 remainder 11 → 18 is not a factor
83 ÷ 19 = 4 remainder 7 → 19 is not a factor
83 ÷ 20 = 4 remainder 3 → 20 is not a factor
83 ÷ 21 = 3 remainder 20 → 21 is not a factor
83 ÷ 22 = 3 remainder 17 → 22 is not a factor
83 ÷ 23 = 3 remainder 14 → 23 is not a factor
83 ÷ 24 = 3 remainder 11 → 24 is not a factor
83 ÷ 25 = 3 remainder 8 → 25 is not a factor
83 ÷ 26 = 3 remainder 5 → 26 is not a factor
83 ÷ 27 = 3 remainder 2 → 27 is not a factor
83 ÷ 28 = 2 remainder 27 → 28 is not a factor
83 ÷ 29 = 2 remainder 25 → 29 is not a factor
83 ÷ 30 = 2 remainder 23 → 30 is not a factor
83 ÷ 31 = 2 remainder 21 → 31 is not a factor
83 ÷ 32 = 2 remainder 19 → 32 is not a factor
83 ÷ 33 = 2 remainder 17 → 33 is not a factor
83 ÷ 34 = 2 remainder 15 → 34 is not a factor
83 ÷ 35 = 2 remainder 13 → 35 is not a factor
83 ÷ 36 = 2 remainder 11 → 36 is not a factor
83 ÷ 37 = 2 remainder 9 → 37 is not a factor
83 ÷ 38 = 2 remainder 7 → 38 is not a factor
83 ÷ 39 = 2 remainder 5 → 39 is not a factor
83 ÷ 40 = 2 remainder 3 → 40 is not a factor
83 ÷ 41 = 2 remainder 1 → 41 is not a factor
83 ÷ 42 = 1 remainder 41 → 42 is not a factor
83 ÷ 43 = 1 remainder 40 → 43 is not a factor
83 ÷ 44 = 1 remainder 39 → 44 is not a factor
83 ÷ 45 = 1 remainder 38 → 45 is not a factor
83 ÷ 46 = 1 remainder 37 → 46 is not a factor
83 ÷ 47 = 1 remainder 36 → 47 is not a factor
83 ÷ 48 = 1 remainder 35 → 48 is not a factor
83 ÷ 49 = 1 remainder 34 → 49 is not a factor
83 ÷ 50 = 1 remainder 33 → 50 is not a factor
83 ÷ 51 = 1 remainder 32 → 51 is not a factor
83 ÷ 52 = 1 remainder 31 → 52 is not a factor
83 ÷ 53 = 1 remainder 30 → 53 is not a factor
83 ÷ 54 = 1 remainder 29 → 54 is not a factor
83 ÷ 55 = 1 remainder 28 → 55 is not a factor
83 ÷ 56 = 1 remainder 27 → 56 is not a factor
83 ÷ 57 = 1 remainder 26 → 57 is not a factor
83 ÷ 58 = 1 remainder 25 → 58 is not a factor
83 ÷ 59 = 1 remainder 24 → 59 is not a factor
83 ÷ 60 = 1 remainder 23 → 60 is not a factor
83 ÷ 61 = 1 remainder 22 → 61 is not a factor
83 ÷ 62 = 1 remainder 21 → 62 is not a factor
83 ÷ 63 = 1 remainder 20 → 63 is not a factor
83 ÷ 64 = 1 remainder 19 → 64 is not a factor
83 ÷ 65 = 1 remainder 18 → 65 is not a factor
83 ÷ 66 = 1 remainder 17 → 66 is not a factor
83 ÷ 67 = 1 remainder 16 → 67 is not a factor
83 ÷ 68 = 1 remainder 15 → 68 is not a factor
83 ÷ 69 = 1 remainder 14 → 69 is not a factor
83 ÷ 70 = 1 remainder 13 → 70 is not a factor
83 ÷ 71 = 1 remainder 12 → 71 is not a factor
83 ÷ 72 = 1 remainder 11 → 72 is not a factor
83 ÷ 73 = 1 remainder 10 → 73 is not a factor
83 ÷ 74 = 1 remainder 9 → 74 is not a factor
83 ÷ 75 = 1 remainder 8 → 75 is not a factor
83 ÷ 76 = 1 remainder 7 → 76 is not a factor
83 ÷ 77 = 1 remainder 6 → 77 is not a factor
83 ÷ 78 = 1 remainder 5 → 78 is not a factor
83 ÷ 79 = 1 remainder 4 → 79 is not a factor
83 ÷ 80 = 1 remainder 3 → 80 is not a factor
83 ÷ 81 = 1 remainder 2 → 81 is not a factor
83 ÷ 82 = 1 remainder 1 → 82 is not a factor
83 ÷ 83 = 1 remainder 0 → 83 is a factor
Yes, 83 is a prime number because it has exactly two factors: 1 and 83.
• 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
84 ÷ 1 = 84 remainder 0 → 1 is a factor
84 ÷ 2 = 42 remainder 0 → 2 is a factor
84 ÷ 3 = 28 remainder 0 → 3 is a factor
84 ÷ 4 = 21 remainder 0 → 4 is a factor
84 ÷ 5 = 16 remainder 4 → 5 is not a factor
84 ÷ 6 = 14 remainder 0 → 6 is a factor
84 ÷ 7 = 12 remainder 0 → 7 is a factor
84 ÷ 8 = 10 remainder 4 → 8 is not a factor
84 ÷ 9 = 9 remainder 3 → 9 is not a factor
84 ÷ 10 = 8 remainder 4 → 10 is not a factor
84 ÷ 11 = 7 remainder 7 → 11 is not a factor
84 ÷ 12 = 7 remainder 0 → 12 is a factor
84 ÷ 13 = 6 remainder 6 → 13 is not a factor
84 ÷ 14 = 6 remainder 0 → 14 is a factor
84 ÷ 15 = 5 remainder 9 → 15 is not a factor
84 ÷ 16 = 5 remainder 4 → 16 is not a factor
84 ÷ 17 = 4 remainder 16 → 17 is not a factor
84 ÷ 18 = 4 remainder 12 → 18 is not a factor
84 ÷ 19 = 4 remainder 8 → 19 is not a factor
84 ÷ 20 = 4 remainder 4 → 20 is not a factor
84 ÷ 21 = 4 remainder 0 → 21 is a factor
84 ÷ 22 = 3 remainder 18 → 22 is not a factor
84 ÷ 23 = 3 remainder 15 → 23 is not a factor
84 ÷ 24 = 3 remainder 12 → 24 is not a factor
84 ÷ 25 = 3 remainder 9 → 25 is not a factor
84 ÷ 26 = 3 remainder 6 → 26 is not a factor
84 ÷ 27 = 3 remainder 3 → 27 is not a factor
84 ÷ 28 = 3 remainder 0 → 28 is a factor
84 ÷ 29 = 2 remainder 26 → 29 is not a factor
84 ÷ 30 = 2 remainder 24 → 30 is not a factor
84 ÷ 31 = 2 remainder 22 → 31 is not a factor
84 ÷ 32 = 2 remainder 20 → 32 is not a factor
84 ÷ 33 = 2 remainder 18 → 33 is not a factor
84 ÷ 34 = 2 remainder 16 → 34 is not a factor
84 ÷ 35 = 2 remainder 14 → 35 is not a factor
84 ÷ 36 = 2 remainder 12 → 36 is not a factor
84 ÷ 37 = 2 remainder 10 → 37 is not a factor
84 ÷ 38 = 2 remainder 8 → 38 is not a factor
84 ÷ 39 = 2 remainder 6 → 39 is not a factor
84 ÷ 40 = 2 remainder 4 → 40 is not a factor
84 ÷ 41 = 2 remainder 2 → 41 is not a factor
84 ÷ 42 = 2 remainder 0 → 42 is a factor
84 ÷ 43 = 1 remainder 41 → 43 is not a factor
84 ÷ 44 = 1 remainder 40 → 44 is not a factor
84 ÷ 45 = 1 remainder 39 → 45 is not a factor
84 ÷ 46 = 1 remainder 38 → 46 is not a factor
84 ÷ 47 = 1 remainder 37 → 47 is not a factor
84 ÷ 48 = 1 remainder 36 → 48 is not a factor
84 ÷ 49 = 1 remainder 35 → 49 is not a factor
84 ÷ 50 = 1 remainder 34 → 50 is not a factor
84 ÷ 51 = 1 remainder 33 → 51 is not a factor
84 ÷ 52 = 1 remainder 32 → 52 is not a factor
84 ÷ 53 = 1 remainder 31 → 53 is not a factor
84 ÷ 54 = 1 remainder 30 → 54 is not a factor
84 ÷ 55 = 1 remainder 29 → 55 is not a factor
84 ÷ 56 = 1 remainder 28 → 56 is not a factor
84 ÷ 57 = 1 remainder 27 → 57 is not a factor
84 ÷ 58 = 1 remainder 26 → 58 is not a factor
84 ÷ 59 = 1 remainder 25 → 59 is not a factor
84 ÷ 60 = 1 remainder 24 → 60 is not a factor
84 ÷ 61 = 1 remainder 23 → 61 is not a factor
84 ÷ 62 = 1 remainder 22 → 62 is not a factor
84 ÷ 63 = 1 remainder 21 → 63 is not a factor
84 ÷ 64 = 1 remainder 20 → 64 is not a factor
84 ÷ 65 = 1 remainder 19 → 65 is not a factor
84 ÷ 66 = 1 remainder 18 → 66 is not a factor
84 ÷ 67 = 1 remainder 17 → 67 is not a factor
84 ÷ 68 = 1 remainder 16 → 68 is not a factor
84 ÷ 69 = 1 remainder 15 → 69 is not a factor
84 ÷ 70 = 1 remainder 14 → 70 is not a factor
84 ÷ 71 = 1 remainder 13 → 71 is not a factor
84 ÷ 72 = 1 remainder 12 → 72 is not a factor
84 ÷ 73 = 1 remainder 11 → 73 is not a factor
84 ÷ 74 = 1 remainder 10 → 74 is not a factor
84 ÷ 75 = 1 remainder 9 → 75 is not a factor
84 ÷ 76 = 1 remainder 8 → 76 is not a factor
84 ÷ 77 = 1 remainder 7 → 77 is not a factor
84 ÷ 78 = 1 remainder 6 → 78 is not a factor
84 ÷ 79 = 1 remainder 5 → 79 is not a factor
84 ÷ 80 = 1 remainder 4 → 80 is not a factor
84 ÷ 81 = 1 remainder 3 → 81 is not a factor
84 ÷ 82 = 1 remainder 2 → 82 is not a factor
84 ÷ 83 = 1 remainder 1 → 83 is not a factor
84 ÷ 84 = 1 remainder 0 → 84 is a factor
Yes, 84 is a composite number because it has more than two factors: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
• Composite Definition: Must have more than two factors
• Factor Pairs: 1×84=84, 2×42=84, 3×28=84, 4×21=84, 6×14=84, 7×12=84
• Counting: More than 2 factors means it's composite
Classification: Determining if each number is prime or composite by finding its factors
Factors: 1, 89 → Prime (exactly 2 factors)
Factors: 1, 7, 13, 91 → Composite (4 factors)
Factors: 1, 3, 31, 93 → Composite (4 factors)
Factors: 1, 97 → Prime (exactly 2 factors)
Factors: 1, 3, 9, 11, 33, 99 → Composite (6 factors)
Prime: 89, 97 | Composite: 91, 93, 99
Prime numbers: 89, 97 | Composite numbers: 91, 93, 99
• 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...
• Every composite number has at least one prime factor
Word problems: Real-world situations requiring knowledge of factors and divisibility
Factors of 97: 1, 97
Option 1: 1 row of 97 books (1×97)
Option 2: 97 rows of 1 book each (97×1)
Since 97 has exactly 2 factors (1 and 97), it's prime
Michael can arrange the books in only 2 ways: 1 row of 97 books or 97 rows of 1 book each
Michael can arrange his 97 books in 1 row of 97 books or 97 rows of 1 book each. The number 97 is prime because it has exactly two factors: 1 and 97.
• Prime Application: Prime numbers have limited arrangement options
• Real-world connection: Arranging objects requires understanding factors
• Verification: Confirm that arrangements use all books
Range analysis: Systematically checking numbers within a specified range
101, 102, 103, 104, 105, 106, 107, 108, 109
Factors: 1, 101 → prime
102 = 2 × 51 → composite
Factors: 1, 103 → prime
104 = 8 × 13 → composite
105 = 3 × 35 → composite
106 = 2 × 53 → composite
Factors: 1, 107 → prime
108 = 4 × 27 → composite
Factors: 1, 109 → prime
The prime numbers between 100 and 110 are: 101, 103, 107, and 109
• 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 Q&A: Questions and answers focusing on identifying numbers with exactly two factors
Composite Number Q&A: Questions and answers focusing on identifying numbers with more than two factors
Classification Q&A: Questions and answers that require distinguishing between prime and composite numbers
- Q&A 1 (Prime): Take number 103 → factors are 1 and 103 → exactly 2 factors → prime
- Q&A 2 (Composite): Take number 105 → factors are 1, 3, 5, 7, 15, 21, 35, 105 → 8 factors → composite
- Q&A 3 (Pattern): Notice that all even numbers > 2 are composite
- Q&A 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