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Greatest Common Factors

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In the lunch room, 36 fith-graders and 27 fourth-graders are sitting in equal groups. All the students in each group are in the same grade.What is the greatest number of students who could be in each group?

  • Greatest Common Factors -

    The fifth-graders could evenly be in
    1 group of 36 ... or
    2 groups of 18 ...or
    3 groups of 12 ... or
    4 groups of 9 ... or
    6 groups of 6 ... or
    9 groups of 4 ...or
    12 groups of 3 ... or
    18 groups of 2 ... or
    36 groups of 1

    The fourth-graders could evenly be in
    1 group of 27...or
    3 groups of 9...or
    9 groups of 3...or
    27 groups of 1
    If they have to have the same number in both groups, they could either have 1, 3 or 9 (the common factors). Since we want the greatest number, which would we choose?

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