Chapter 3 — cumulative chapter review
Semester 4A · Chapter 3 · 33 questions
This review integrates every chapter learning objective. Try questions before revealing answers.
Find the 5th positive multiple of 9.
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9 × 5 = 45.
Find the least positive common multiple of 7 and 13.
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List positive multiples of each or use prime factors to locate the first shared positive multiple: 91.
List all positive factors of 128.
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Each factor divides 128 with no remainder; pair divisors with their matching quotients.
Classify 49 as prime, composite, or neither.
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The positive factors are 1, 7, 49. Prime means exactly two positive factors; 1 is neither prime nor composite.
What is the greatest common factor of 18 and 39?
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The GCF is the largest whole number dividing both with no remainder: 3.
Find the 2nd positive multiple of 12.
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12 × 2 = 24.
Will 126 be a common multiple of 9 and 7? Explain.
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126 is two times their least common multiple, so both numbers divide it.
List all positive factors of 20.
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Each factor divides 20 with no remainder; pair divisors with their matching quotients.
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.
What is the greatest common factor of 20 and 33?
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The GCF is the largest whole number dividing both with no remainder: 1.
Find the 3rd positive multiple of 10.
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10 × 3 = 30.
Find the least positive common multiple of 6 and 12.
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List positive multiples of each or use prime factors to locate the first shared positive multiple: 12.
Is 3 a factor of 27? Give a reason.
Show answer & reasoning
27 ÷ 3 = 9, a whole number.
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.
What is the greatest common factor of 8 and 33?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 1.
Find the 5th positive multiple of 15.
Show answer & reasoning
15 × 5 = 75.
Find the least positive common multiple of 8 and 7.
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List positive multiples of each or use prime factors to locate the first shared positive multiple: 56.
List all positive factors of 72.
Show answer & reasoning
Each factor divides 72 with no remainder; pair divisors with their matching quotients.
Classify 32 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 2, 4, 8, 16, 32. Prime means exactly two positive factors; 1 is neither prime nor composite.
What is the greatest common factor of 10 and 24?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 2.
Find the 7th positive multiple of 8.
Show answer & reasoning
8 × 7 = 56.
Will 420 be a common multiple of 14 and 15? Explain.
Show answer & reasoning
420 is two times their least common multiple, so both numbers divide it.
List all positive factors of 64.
Show answer & reasoning
Each factor divides 64 with no remainder; pair divisors with their matching quotients.
Classify 77 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 7, 11, 77. Prime means exactly two positive factors; 1 is neither prime nor composite.
What is the greatest common factor of 8 and 45?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 1.
Is zero a multiple of 16? Explain.
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0 = 16 × 0, so zero is a multiple of 16.
Find the least positive common multiple of 5 and 5.
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List positive multiples of each or use prime factors to locate the first shared positive multiple: 5.
Is zero a multiple of 6? Explain using multiplication.
Show answer & reasoning
6 × 0 = 0. A multiple includes zero when the multiplier is a whole number.
A student says 48 is the least positive common multiple of 6 and 8 because both divide it. Find the actual least positive common multiple.
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24 is the first positive multiple shared by 6 and 8; 48 is a later common multiple.
A learner says 12 has only factors 2, 3, and 4. Explain the omitted factors and list all positive factors.
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Factor pairs of 12 are (1,12), (2,6), and (3,4).
Sam claims 13 is prime because it is not divisible by 5. Explain why that test is insufficient, and classify 13.
Show answer & reasoning
Not being divisible by 5 proves nothing by itself. The factors of 13 are 1, 13. A prime has exactly two positive factors.
A learner says the greatest common factor of 12 and 18 is 36 because both multiply into 36. Find the GCF.
Show answer & reasoning
A common factor divides both numbers; 6 is the largest positive divisor shared by 12 and 18.
Is zero a multiple of 9? Explain using multiplication.
Show answer & reasoning
9 × 0 = 0. A multiple includes zero when the multiplier is a whole number.