1 is neither prime nor composite (it only has one factor). 2 is the only even prime number. 0 has every number as a factor but is neither prime nor composite.
Students often say "1 is prime because it's only divisible by 1 and itself."
Explain: Prime numbers have EXACTLY two distinct factors. 1 only has ONE factor (itself), so it doesn't meet the definition. 1 is special - it's neither prime nor composite.
Students find some factor pairs but miss others. For 24, they might find (1,24) and (2,12) but miss (3,8) or (4,6).
Teach systematic factor finding: Start with 1, then try 2, 3, 4... Stop when you reach a factor pair you've already found. Use arrays to visualize all possible rectangles.
Students mix up "factors of 12" with "multiples of 12." They might list 24 and 36 as factors of 12.
Use the analogy: Factors DIVIDE evenly (they're smaller or equal). Multiples are PRODUCTS (they grow bigger). "Factors fit INTO, Multiples GROW OUT OF."
Give students 12 square tiles. Ask: "How many different rectangles can you make using all 12 tiles?"
"Each rectangle shows a factor pair! A 3x4 rectangle shows that 3 and 4 are both factors of 12. What other rectangles can you make?"
Model finding all factors of 36:
| Try | Does it divide evenly? | Factor Pair |
|---|---|---|
| 1 | Yes (36 / 1 = 36) | (1, 36) |
| 2 | Yes (36 / 2 = 18) | (2, 18) |
| 3 | Yes (36 / 3 = 12) | (3, 12) |
| 4 | Yes (36 / 4 = 9) | (4, 9) |
| 5 | No (36 / 5 = 7.2) | - |
| 6 | Yes (36 / 6 = 6) | (6, 6) STOP! |
Show that some numbers make only ONE rectangle (prime) while others make multiple rectangles (composite).
"7 can only make a 1x7 rectangle - it has exactly 2 factors, so it's PRIME. 12 can make several rectangles (1x12, 2x6, 3x4) - it has more than 2 factors, so it's COMPOSITE."
Show the inverse relationship: If 4 is a factor of 12, then 12 is a multiple of 4.
List multiples by skip counting: Multiples of 6: 6, 12, 18, 24, 30...
Find common multiples: Multiples of 4 AND 6: 12, 24, 36... (LCM = 12)
Distribute worksheets. Remind students to be systematic - check ALL possible factors, and remember the special cases (1 is neither prime nor composite).
For struggling students: Focus on numbers to 30 first. Use physical tiles for all factor-finding. Provide a multiplication chart for reference.
For advanced students: Extend to finding GCF and LCM. Explore factor trees and prime factorization. Challenge with numbers beyond 100.
For home: Play "Factor Game" - pick a number, take turns naming factors. First person who can't name a new factor loses!