Prime and Composite Numbers Worksheets with Complete Answers

Complete collection of worksheets with detailed answers covering prime and composite numbers, factors, multiples, and number patterns for grades 4-6. Includes step-by-step solutions and comprehensive explanations.

Worksheets 1 to 3: With Complete Answers
1 Prime Number Identification
Worksheet 1: Prime Number Basics
Instructions: Circle all prime numbers in each set below. Use the definition of prime numbers to help you.

Set A: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Set B: 12, 13, 14, 15, 16, 17, 18, 19, 20, 21
Set C: 22, 23, 24, 25, 26, 27, 28, 29, 30, 31
Definition:

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

Key Point: 1 is neither prime nor composite

Method to identify primes:
  1. Check if the number is greater than 1
  2. List all factors of the number
  3. If exactly 2 factors → Prime
  4. If more than 2 factors → Composite
Set A
2, 3, 5, 7, 11
Set B
13, 17, 19
Set C
23, 29, 31
Step 1: Set A Analysis

2: Factors {1, 2} → Prime ✅

3: Factors {1, 3} → Prime ✅

4: Factors {1, 2, 4} → Composite ❌

5: Factors {1, 5} → Prime ✅

6: Factors {1, 2, 3, 6} → Composite ❌

7: Factors {1, 7} → Prime ✅

8: Factors {1, 2, 4, 8} → Composite ❌

9: Factors {1, 3, 9} → Composite ❌

10: Factors {1, 2, 5, 10} → Composite ❌

11: Factors {1, 11} → Prime ✅

Step 2: Set B Analysis

12: Factors {1, 2, 3, 4, 6, 12} → Composite ❌

13: Factors {1, 13} → Prime ✅

14: Factors {1, 2, 7, 14} → Composite ❌

15: Factors {1, 3, 5, 15} → Composite ❌

16: Factors {1, 2, 4, 8, 16} → Composite ❌

17: Factors {1, 17} → Prime ✅

18: Factors {1, 2, 3, 6, 9, 18} → Composite ❌

19: Factors {1, 19} → Prime ✅

20: Factors {1, 2, 4, 5, 10, 20} → Composite ❌

21: Factors {1, 3, 7, 21} → Composite ❌

Step 3: Set C Analysis

22: Factors {1, 2, 11, 22} → Composite ❌

23: Factors {1, 23} → Prime ✅

24: Factors {1, 2, 3, 4, 6, 8, 12, 24} → Composite ❌

25: Factors {1, 5, 25} → Composite ❌

26: Factors {1, 2, 13, 26} → Composite ❌

27: Factors {1, 3, 9, 27} → Composite ❌

28: Factors {1, 2, 4, 7, 14, 28} → Composite ❌

29: Factors {1, 29} → Prime ✅

30: Factors {1, 2, 3, 5, 6, 10, 15, 30} → Composite ❌

31: Factors {1, 31} → Prime ✅

Set A: 2, 3, 5, 7, 11
Set B: 13, 17, 19
Set C: 23, 29, 31
Answer Key:

Set A: Prime numbers are 2, 3, 5, 7, 11

Set B: Prime numbers are 13, 17, 19

Set C: Prime numbers are 23, 29, 31

Complete Solution with Detailed Steps!

Key Rules:

• Prime Rule: Has exactly two factors: 1 and itself

• Composite Rule: Has more than two factors

• Special Case: 1 is neither prime nor composite

2 Finding Factors and Multiples
Worksheet 2: Factors and Multiples
Instructions: Find all factors of each number and list the first 5 multiples.

Number 1: 24
Number 2: 36
Number 3: 48
Definition:

Factor: A number that divides another number evenly with no remainder

Multiple: The product of a number and any integer

Number
24
Factors
1, 2, 3, 4, 6, 8, 12, 24
Multiples
24, 48, 72, 96, 120
Step 1: Find all factors of 24

Start with 1: 1 × 24 = 24 → Factors: 1, 24

Try 2: 2 × 12 = 24 → Factors: 2, 12

Try 3: 3 × 8 = 24 → Factors: 3, 8

Try 4: 4 × 6 = 24 → Factors: 4, 6

Try 5: 5 doesn't divide 24 evenly

Stop when factors repeat (we already have 6)

All factors: {1, 2, 3, 4, 6, 8, 12, 24}

Step 2: Find first 5 multiples of 24

24 × 1 = 24

24 × 2 = 48

24 × 3 = 72

24 × 4 = 96

24 × 5 = 120

First 5 multiples: {24, 48, 72, 96, 120}

Step 3: Find all factors of 36

1 × 36 = 36, 2 × 18 = 36, 3 × 12 = 36, 4 × 9 = 36, 6 × 6 = 36

All factors: {1, 2, 3, 4, 6, 9, 12, 18, 36}

Step 4: Find all factors of 48

1 × 48 = 48, 2 × 24 = 48, 3 × 16 = 48, 4 × 12 = 48, 6 × 8 = 48

All factors: {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

24: Factors {1,2,3,4,6,8,12,24}, Multiples {24,48,72,96,120}
36: Factors {1,2,3,4,6,9,12,18,36}, Multiples {36,72,108,144,180}
48: Factors {1,2,3,4,6,8,12,16,24,48}, Multiples {48,96,144,192,240}
Answer Key:

Number 24: Factors {1, 2, 3, 4, 6, 8, 12, 24}, Multiples {24, 48, 72, 96, 120}

Number 36: Factors {1, 2, 3, 4, 6, 9, 12, 18, 36}, Multiples {36, 72, 108, 144, 180}

Number 48: Factors {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}, Multiples {48, 96, 144, 192, 240}

Complete Solution with Detailed Steps!

Applied rules:

• Systematic Method: Check divisors from 1 upward

• Factor Pair Strategy: Find two numbers that multiply to target

• Stopping Point: Stop when factors start repeating

3 Prime vs Composite Identification
Worksheet 3: Prime vs Composite
Instructions: Classify each number as prime or composite. Explain your reasoning.

Numbers: 17, 21, 29, 33, 37, 41, 45, 49
Definition:

Quick Prime Test: Try dividing by 2, 3, 5, 7, 11, etc. up to √n

Numbers
17, 21, 29, 33, 37, 41, 45, 49
Classification
Mixed
Step 1: Test 17

Check divisibility by small primes: 2, 3, 5

17 ÷ 2 = 8.5 (not whole)

17 ÷ 3 = 5.67 (not whole)

17 ÷ 5 = 3.4 (not whole)

No divisors found → 17 is prime

Step 2: Test 21

21 ÷ 3 = 7 (whole number)

So 21 = 3 × 7 → 21 has factors 1, 3, 7, 21

More than 2 factors → 21 is composite

Step 3: Test 29

Check divisibility by 2, 3, 5

29 ÷ 2 = 14.5 (not whole)

29 ÷ 3 = 9.67 (not whole)

29 ÷ 5 = 5.8 (not whole)

No divisors found → 29 is prime

Step 4: Test 33

33 ÷ 3 = 11 (whole number)

So 33 = 3 × 11 → 33 has factors 1, 3, 11, 33

More than 2 factors → 33 is composite

Step 5: Test 37

Check divisibility by 2, 3, 5

37 ÷ 2 = 18.5 (not whole)

37 ÷ 3 = 12.33 (not whole)

37 ÷ 5 = 7.4 (not whole)

No divisors found → 37 is prime

Step 6: Test 41

Check divisibility by 2, 3, 5

41 ÷ 2 = 20.5 (not whole)

41 ÷ 3 = 13.67 (not whole)

41 ÷ 5 = 8.2 (not whole)

No divisors found → 41 is prime

Step 7: Test 45

45 ÷ 3 = 15 (whole number)

So 45 = 3 × 15 → 45 has factors 1, 3, 5, 9, 15, 45

More than 2 factors → 45 is composite

Step 8: Test 49

49 ÷ 7 = 7 (whole number)

So 49 = 7 × 7 → 49 has factors 1, 7, 49

More than 2 factors → 49 is composite

Prime: 17, 29, 37, 41
Composite: 21, 33, 45, 49
Answer Key:

Prime numbers: 17, 29, 37, 41

Composite numbers: 21, 33, 45, 49

Complete Solution with Detailed Steps!

Applied rules:

• Prime Testing: Check divisibility by small primes up to √n

• Even Numbers: All even numbers > 2 are composite

• Divisibility Rules: Use quick checks for 2, 3, 5

Complete Answer Keys & Solutions
Prime: Exactly 2 factors
Definition
Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
First 15 prime numbers
Composite Numbers
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25
First 15 composite numbers
Special Cases
1 = Neither Prime Nor Composite
Unique classification
Key definitions:

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

Factor: A number that divides another number evenly with no remainder

Multiple: The product of a number and any integer

Complete methodology:
  1. Identify the number: Look at the target number to test
  2. Find all factors: List factor pairs systematically
  3. Count factors: Determine how many factors exist
  4. Classify: If exactly 2 factors → Prime, if more than 2 → Composite
Tip 1: 2 is the only even prime number. All other even numbers are composite.
Tip 2: Numbers ending in 5 (except 5 itself) are always composite.
Tip 3: To test if large numbers are prime, only check divisibility up to √n.
Tip 4: 1 is neither prime nor composite - it's a special case!
Common errors: Forgetting that 1 is neither prime nor composite, thinking even numbers can be prime (except 2).
Memory aid: "Prime" sounds like "primary" - the basic building blocks of numbers.
Essential facts to remember:

• Smallest prime number: 2

• Only even prime: 2

• 1 is neither prime nor composite

• Prime numbers are the "building blocks" of all numbers

• Every composite number can be made by multiplying prime numbers

Answer Verification:

Complete Answer Keys Included:

  • Worksheet 1: Prime Number Identification - All answers provided
  • Worksheet 2: Factors and Multiples - Complete factor lists
  • Worksheet 3: Prime vs Composite - Detailed classifications
  • Worksheet 4: Prime Factorization - Step-by-step solutions
  • Worksheet 5: Real-World Problems - Complete worked solutions

Every answer includes detailed reasoning and verification!

Worksheets 4 to 5: Advanced with Answers
4 Prime Factorization Practice
Worksheet 4: Prime Factorization
Instructions: Find the prime factorization of each number using factor trees. Show your work.

Number 1: 36
Number 2: 48
Number 3: 60
Number 4: 72
Number 5: 84
Definition:

Prime Factorization: Expressing a composite number as a product of prime numbers

Number
36
Factorization
2²×3²
Step 1: Prime factorization of 36

36 = 4 × 9

4 = 2 × 2, 9 = 3 × 3

So 36 = 2 × 2 × 3 × 3 = 2² × 3²

Step 2: Prime factorization of 48

48 = 6 × 8

6 = 2 × 3, 8 = 2 × 4 = 2 × 2 × 2

So 48 = 2 × 3 × 2 × 2 × 2 = 2⁴ × 3

Step 3: Prime factorization of 60

60 = 6 × 10

6 = 2 × 3, 10 = 2 × 5

So 60 = 2 × 3 × 2 × 5 = 2² × 3 × 5

Step 4: Prime factorization of 72

72 = 8 × 9

8 = 2 × 2 × 2, 9 = 3 × 3

So 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

Step 5: Prime factorization of 84

84 = 4 × 21

4 = 2 × 2, 21 = 3 × 7

So 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7

36 = 2² × 3²
48 = 2⁴ × 3
60 = 2² × 3 × 5
72 = 2³ × 3²
84 = 2² × 3 × 7
Answer Key:

36 = 2² × 3²

48 = 2⁴ × 3

60 = 2² × 3 × 5

72 = 2³ × 3²

84 = 2² × 3 × 7

Complete Solution with Detailed Steps!

Applied rules:

• Prime Factorization: Break down until only primes remain

• Factor Trees: Visual method to organize factorization

• Verification: Multiply factors back to check

5 Real-World Applications
Worksheet 5: Problem Solving
Instructions: Solve each word problem using prime and composite number concepts.

Problem 1: Sarah has 24 cookies and wants to arrange them in equal rows. How many different arrangements are possible?
Problem 2: Two friends start running. One completes a lap every 12 minutes, the other every 18 minutes. When will they meet again at the starting point?
Definition:

Real-world Applications: Using factors and multiples to solve practical problems

Problem 1
24 cookies
Arrangements
8 ways
Problem 2
LCM(12,18)
Step 1: Problem 1 Solution

Find all factors of 24 to determine possible arrangements

Factors of 24: {1, 2, 3, 4, 6, 8, 12, 24}

Possible arrangements:

1 row × 24 columns

2 rows × 12 columns

3 rows × 8 columns

4 rows × 6 columns

6 rows × 4 columns

8 rows × 3 columns

12 rows × 2 columns

24 rows × 1 column

Total: 8 different arrangements

Step 2: Problem 2 Solution

Find LCM of 12 and 18 to determine when they meet

12 = 2² × 3

18 = 2 × 3²

LCM = 2² × 3² = 4 × 9 = 36

They will meet again after 36 minutes

Problem 1: 8 arrangements
Problem 2: 36 minutes
Answer Key:

Problem 1: Sarah can arrange her 24 cookies in 8 different ways using the factors of 24.

Problem 2: The two friends will meet again at the starting point after 36 minutes.

Complete Solution with Detailed Steps!

Applied rules:

• Real-world Application: Factors relate to arranging objects

• LCM Rule: For simultaneous events, use LCM of intervals

• Verification: Always check calculations

Complete Answer Guide & Study Notes
Prime: Exactly 2 factors
Core Property
Prime Patterns
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Primes up to 50
Composite Patterns
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25
Composites up to 25
Prime Testing
Check divisors up to √n
Efficient method
Complete definitions:

Prime Number: A natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself

Composite Number: A natural number greater than 1 that has more than two distinct positive divisors

Prime Factorization: Expressing a composite number as a unique product of prime numbers raised to powers

Factor: A number that divides another number evenly with no remainder

Multiple: The product of a number and any integer

Complete methodologies:
  1. Prime Testing: Systematic divisibility checks up to √n
  2. Factor Trees: Visual decomposition into prime factors
  3. Division Method: Repeated division by primes
  4. Real-world Applications: Using factors and multiples to solve problems
Tip 1: Use divisibility rules to quickly eliminate composites.
Tip 2: Twin primes are primes that differ by 2 (like 11 and 13).
Tip 3: The number of primes decreases as numbers get larger.
Tip 4: Every number can be expressed as a unique product of primes.
Interesting Fact: There are infinitely many prime numbers - proven by Euclid!
Real-world Use: Primes are essential for computer security and encryption.
Important rules for memorization:

• All primes > 3 are of the form 6n±1

• The sum of digits test: if sum divisible by 3, number divisible by 3

• If last digit is 0 or 5, number divisible by 5

• Prime factorization is unique for every number

• There are 25 primes less than 100

Study Notes:

Complete Answer Guide Features:

  • Detailed step-by-step solutions for every problem
  • Explanation of the reasoning behind each answer
  • Alternative methods and approaches
  • Common mistake identification
  • Verification techniques
  • Key concept summaries

All answers include detailed explanations for better understanding!

Frequently Asked Questions

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