CCSS.MATH.4.OA.B.4✓ NSW Education Standards Authority (NESA) AlignedAcademic Year 2026–27
Factors, Multiples, Prime & Composite Numbers
Discover factor pairs using rectangular arrays and categorize integers 1–100 into prime and composite sets.
Why It Matters:Foundational for simplifying fractions, finding common denominators, and modern cryptographic security.
Curated Video Instruction
● Verified Active EmbedSTEP-BY-STEP PROOF
Worked Example
Find all factor pairs for 36 and classify 36 as prime or composite:
1
Systematically test integer divisors starting from 1
1 * 36 = 36; 2 * 18 = 36; 3 * 12 = 36; 4 * 9 = 36; 6 * 6 = 36
Test divisors up to the square root of 36 (√36 = 6).
2
List all unique factors
Factors of 36: {1, 2, 3, 4, 6, 9, 12, 18, 36}
Combine all distinct divisor pairs.
3
Classify as prime or composite
36 has 9 factors (> 2 factors) → Composite
A prime number has exactly two distinct factors: 1 and itself.
✓Verification Check
Confirm 36 is composite because it has factors other than 1 and 36.
Count of factors = 9
•
9 > 2 (Composite Verified)
⚠️ Common Pitfalls & Misconceptions
Believing 1 is a prime number
✗ Calling 1 prime because it has no divisors other than 1✓ 1 is neither prime nor composite because it has only ONE factor
By mathematical definition, prime numbers must have EXACTLY two distinct positive factors.
INTERACTIVE DRILLS
Guided Practice
Practice Question1 of 1
Step-by-step Feedback
Which of the following numbers is a PRIME number?
MASTERY BENCHMARK
Official Assessment Quiz
Formal Assessment
Factors, Multiples, Prime & Composite Numbers
Passing Criteria:70% or higher
Question 1 of 1
What are all the factors of 12?
Education to Career Navigation
Where This Lesson Leads
Cryptographers and Cyber Security Specialists use prime factorization to encrypt financial transactions.