Prime Numbers and Composite Numbers
4A · Chapter 3 · Lesson 4 · MATH-4A-C03-L04
Learning goal. Classify positive integers using their factor structure and explain exceptions for 0 and 1.
Before you begin
Recall: Grade 3: arrays and multiplication tables; 4A Ch2: addition strategies; Factors. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
List all positive factors of 90.
Show answer & reasoning
Each factor divides 90 with no remainder; pair divisors with their matching quotients.
List all positive factors of 36.
Show answer & reasoning
Each factor divides 36 with no remainder; pair divisors with their matching quotients.
List all positive factors of 130.
Show answer & reasoning
Each factor divides 130 with no remainder; pair divisors with their matching quotients.
Key vocabulary
- multiple
- whole-number product of a given number
- factor
- whole number dividing exactly
- prime
- positive number with exactly two positive factors
- composite
- positive number with more than two positive factors
Understand the concept
A prime number has exactly two distinct positive factors: one and itself. A composite number has more than two positive factors. Seven is prime, whereas nine has 1, 3, and 9 so it is composite. One is neither; zero is also neither. Test possible factors instead of deciding from the numeral's appearance.
Model it: factor arrays and prime/composite sorting. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
Classify 17 as prime, composite, or neither.
The positive factors are 1, 17. Prime means exactly two positive factors; 1 is neither prime nor composite.
Check your understanding 1
Classify 71 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 71. Prime means exactly two positive factors; 1 is neither prime nor composite.
Worked example 2
Classify 58 as prime, composite, or neither.
The positive factors are 1, 2, 29, 58. Prime means exactly two positive factors; 1 is neither prime nor composite.
Check your understanding 2
Classify 57 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 3, 19, 57. Prime means exactly two positive factors; 1 is neither prime nor composite.
Worked example 3
Classify 31 as prime, composite, or neither.
The positive factors are 1, 31. Prime means exactly two positive factors; 1 is neither prime nor composite.
Check your understanding 3
Classify 29 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 29. Prime means exactly two positive factors; 1 is neither prime nor composite.
Guided practice
Classify 46 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 2, 23, 46. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 10 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 2, 5, 10. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 26 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 2, 13, 26. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 7 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 7. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 1 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1. Prime means exactly two positive factors; 1 is neither prime nor composite.
Independent practice
Classify 30 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 2, 3, 5, 6, 10, 15, 30. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 76 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 2, 4, 19, 38, 76. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 43 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 43. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 21 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 3, 7, 21. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 55 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 5, 11, 55. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 42 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 2, 3, 6, 7, 14, 21, 42. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 79 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 79. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 56 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 2, 4, 7, 8, 14, 28, 56. Prime means exactly two positive factors; 1 is neither prime nor composite.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
Sam claims 26 is prime because it is not divisible by 5. Explain why that test is insufficient, and classify 26.
Show answer & reasoning
Not being divisible by 5 proves nothing by itself. The factors of 26 are 1, 2, 13, 26. A prime has exactly two positive factors.
Classify 69 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 3, 23, 69. Prime means exactly two positive factors; 1 is neither prime nor composite.
Exit check
Classify 22 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 2, 11, 22. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 44 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 2, 4, 11, 22, 44. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 39 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 3, 13, 39. Prime means exactly two positive factors; 1 is neither prime nor composite.