Testinar Grade 6 math

Greatest Common Factor and Least Common Multiple

Students will build Grade 6 mastery of greatest common factor and least common multiple using models, equations, and test-style reasoning.

CH02-04 The Number System
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. What is the greatest common factor (GCF) of \(24\) and \(36\)?

    1. \(6\)
    2. \(8\)
    3. \(12\)
    4. \(24\)

  2. Which list contains all factors of \(20\)?

    1. \(1, 2, 4, 5, 10, 20\)
    2. \(1, 2, 3, 4, 5, 20\)
    3. \(2, 4, 5, 10\)
    4. \(1, 2, 4, 5, 8, 20\)

  3. What is the least common multiple (LCM) of \(6\) and \(8\)?

    1. \(24\)
    2. \(18\)
    3. \(14\)
    4. \(48\)

  4. Which pair of numbers has a GCF of \(5\)?

    1. \(15\) and \(25\)
    2. \(10\) and \(20\)
    3. \(12\) and \(20\)
    4. \(14\) and \(35\)

  5. What is the GCF of \(16\) and \(40\)?

    1. \(4\)
    2. \(20\)
    3. \(16\)
    4. \(8\)

  6. Which is a multiple of both \(4\) and \(6\)?

    1. \(8\)
    2. \(12\)
    3. \(18\)
    4. \(10\)

  7. What is the GCF of \(18\), \(27\), and \(45\)?

    1. \(3\)
    2. \(9\)
    3. \(6\)
    4. \(18\)

  8. What is the prime factorization of \(30\)?

    1. \(2 \times 3 \times 5\)
    2. \(2 \times 15\)
    3. \(3 \times 10\)
    4. \(2 \times 2 \times 3\)
Teacher and parent reference

Answer key and explanations

  1. C. \(12\)

    List what both numbers share evenly: candidates include \(12\), since \(24 = 12 \times 2\) and \(36 = 12 \times 3\). Nothing larger divides both cleanly, so the GCF settles at \(12\).

  2. A. \(1, 2, 4, 5, 10, 20\)

    When we divide \(20\) by each number: \(20 \div 1 = 20\), \(20 \div 2 = 10\), \(20 \div 4 = 5\), \(20 \div 5 = 4\), \(20 \div 10 = 2\), \(20 \div 20 = 1\). All these are factors.

  3. A. \(24\)

    Multiples of \(6\): \(6, 12, 18, 24, 30, \ldots\). Multiples of \(8\): \(8, 16, 24, 32, \ldots\). The least common multiple is \(24\).

  4. A. \(15\) and \(25\)

    Factors of \(15\): \(1, 3, 5, 15\). Factors of \(25\): \(1, 5, 25\). Common factors: \(1, 5\). GCF is \(5\). For option B, GCF is \(10\); for C, GCF is \(4\); for D, GCF is \(7\).

  5. D. \(8\)

    Factors of \(16\): \(1, 2, 4, 8, 16\). Factors of \(40\): \(1, 2, 4, 5, 8, 10, 20, 40\). The greatest common factor is \(8\).

  6. B. \(12\)

    \(12 = 4 \times 3\) and \(12 = 6 \times 2\), so \(12\) is divisible by both \(4\) and \(6\). Option A is a multiple of \(4\) but not \(6\); C is a multiple of \(6\) but not \(4\); D is neither.

  7. B. \(9\)

    Factors of \(18\): \(1, 2, 3, 6, 9, 18\). Factors of \(27\): \(1, 3, 9, 27\). Factors of \(45\): \(1, 3, 5, 9, 15, 45\). Common to all three: \(1, 3, 9\). GCF is \(9\).

  8. A. \(2 \times 3 \times 5\)

    \(30 = 2 \times 15 = 2 \times 3 \times 5\). The prime factors are \(2, 3, 5\). Option B uses \(15\), which is composite; C uses \(10\), which is composite; D gives prime factorization of \(12\).

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