GCF, LCM, and Prime Factorization Quiz

Grade 6 · Math · Quiz

Test your knowledge of prime factorization, GCF, and LCM.

Questions

Which number is prime?
1. 17
2. 21
3. 15
4. 9
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Answer: 17
17 is only divisible by 1 and 17. 21=3×7, 15=3×5, 9=3×3 are all composite.
The prime factorization of 18 is 2 × ___.
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Answer: 3²
18 = 2 × 9 = 2 × 3². So the full prime factorization is 2 × 3².
What is the GCF of 24 and 36?
1. 12
2. 6
3. 72
4. 4
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Answer: 12
24 = 2³×3, 36 = 2²×3². GCF uses minimum exponents: 2²×3 = 4×3 = 12.
The LCM of two numbers is always greater than or equal to the larger number.
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Answer: True
Both numbers are multiples of the LCM — so it must be at least as large as the larger number.
What is the LCM of 5 and 8?
1. 40
2. 3
3. 13
4. 80
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Answer: 40
5 and 8 share no common factors. LCM = 5×8 = 40. Check: 40÷5=8 ✓ 40÷8=5 ✓
The GCF of 45 and 60 is ___.
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Answer: 15
45 = 3²×5, 60 = 2²×3×5. GCF uses minimum exponents: 3×5 = 15.
Which is the prime factorization of 60?
1. 2² × 3 × 5
2. 4 × 15
3. 2 × 30
4. 6 × 10
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Answer: 2² × 3 × 5
60 = 2×30 = 2×2×15 = 2×2×3×5 = 2²×3×5. All factors are prime.
GCF(7, 11) = 1 because 7 and 11 are both prime.
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Answer: True
Two different prime numbers have no shared prime factors, so their only common factor is 1.
Layla has 12 red beads and 16 blue beads. She wants to put equal amounts of each color in bags with no beads left over. What is the most beads of one color per bag?
1. 4
2. 2
3. 12
4. 48
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Answer: 4
This is asking for GCF(12, 16). Factors: 12→1,2,3,4,6,12; 16→1,2,4,8,16. GCF=4.
What is the LCM of 6 and 9?
1. 18
2. 54
3. 3
4. 63
Show answer
Answer: 18
Multiples of 6: 6,12,18. Multiples of 9: 9,18. First match is 18.

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