Prime Patrol Worksheet
Prime Patrol: Factor Detective
Number Theory • Factor Pairs & Classification Lab
Name:
Date:
Score:
Prime Number
A whole number greater than 1 with exactly two distinct factors: 1 and itself.
Ex: 7 → (1 × 7) • Only 2 factors
Composite Number
A whole number greater than 1 with more than two factors (can be split into equal groups).
Ex: 12 → 1, 2, 3, 4, 6, 12 • 6 factors
Special Rules
0 and 1 are neither prime nor composite. 2 is the only even prime number!
1 has only 1 factor • 2 has factors 1, 2
Strategy Find factor pairs systematically in order: test 1, 2, 3, 4, 5... until pairs repeat!
18: 1×18, 2×9, 3×6 → Composite
1 Part 1: Factor Finder & Classification Table
List all pairs, count unique factors, and check Prime or Composite.
| Number | All Factor Pairs (e.g., 1 × 16) | All Factors in Order | Factor Count | Classification |
|---|
| 16 | 1 × 16, 2 × 8, 4 × 4 | 1, 2, 4, 8, 16 | 5 | Composite |
| 17 | | | | |
| Prime Comp. | | | | |
|
| 24 | | | |
Prime Comp.
|
| 31 | | | |
Prime Comp.
|
| 45 | | | |
Prime Comp.
|
| 51 | | | |
Prime Comp.
|
2 Part 2: The Number Vault Sorting Challenge
Test factor pairs mentally, then sort each number into the correct vault.
Numbers to Sort:
2 9 15 19 21 29 33 37 49 53
Prime Vault (5 Numbers) Only 1 pair of factors
Write each prime number and its single factor pair (e.g., 2: 1 × 2):
Composite Safe (5 Numbers) At least 2 pairs of factors
Write each composite number and at least two of its factor pairs:
Prime Patrol Math Investigation • Grade 4-6 Page 1 of 2 → Continue to Case Explanations
Case Explanations & Factor Proofs
Construct written mathematical arguments using factor pairs
Student Name:
Page 2
3 Part 3: Truth or Myth? Prove with Factor Pairs
Circle True or False, then write a factor pair proof or counter-example.
Claim A: "Every odd number greater than 1 is a prime number."
TRUE FALSE
Prove your answer by writing an odd number and all of its factor pairs:
Claim B: "All even numbers are composite numbers because they can be divided by 2."
TRUE FALSE
Prove your answer by identifying the one counter-example and its factor pairs:
Claim C: "A composite number can have an odd number of total factors (such as 3 or 5 factors)."
TRUE FALSE
Prove your answer by testing a square number (like 9, 25, or 36) and listing its factors:
4 Part 4: Mathematical Arguments & Explanations
Use complete sentences and factor pair evidence.
The Case of 57
A student claims: "57 is an odd number and ends in 7, so it must be prime!" Explain why this student is wrong. Find the hidden factor pair that proves 57 is composite:
Why Isn't 1 Prime?
Explain why mathematicians classify the number 1 as neither prime nor composite. Use the official definition of prime factors in your answer:
Part 5: Prime Detective Final Mystery
Bonus Challenge
Crack the Mystery Number using these 4 clues:
- I am a two-digit whole number between 20 and 40.
- I am a composite number.
- One of my factor pairs consists of two identical numbers (\(n \times n\)).
- The sum of my two digits is 7.
Mystery Number:
Show Your Factor Pair Proof:
Prime Patrol Math Investigation • Grade 4-6 Completed Case File • All Work Shown
