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