How to Solve a Math Factor Puzzle

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One of the ways that learning mathematics in grade school can be made interesting is through the use of puzzles and games. The factor puzzle is one popular choice that teachers may use while students are learning about multiplication and number factoring. The common setup will be a square that is divided into equal sections. Some of the sections will contain numbers, while the others are blank. The task left to the student is to fill in the blank squares by finding the common characteristics of the given numbers.

    Your factor puzzle will contain some given numbers. For example, a 2-by-2 square may contain the numbers 20, 12 and 21. In each square, list the factors of the number in that square. For example, the factors of 20 are 1, 2, 4, 5, 10 and 20. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 21 are 1, 3, 7 and 21.

    Find the common factors for a given row and column. In the same example, the common factors between 20 and 12 are 2 and 4, while the common factor between 12 and 21 is 3. We'll disregard 1 because it's shared by all numbers.

    Fill in the two numbers in the blank square that are shared by the neighboring sections. In this example, the blank square receives a 5 that it shares with the 20 and a 7 that it shares with 21.

    Multiply the shared common factors to determine the identity of the blank section. In this example, the answer is 35 (7 x 5).

    Things You'll Need

    • Factor puzzle
    • Pencil
    • Paper


    • For squares with increasing numbers of blank sections, you will have to try a different combination of common factors until you find the correct solution.


About the Author

Erik Andrews began scientific and medical writing in 2004. His work as a second author on a research article appeared in the journal "Genetics" in 2005. His areas of expertise are the natural sciences, medical education and physical fitness. He earned a Master of Science in chemistry and a Bachelor of Arts in biochemistry, both from the University of Pennsylvania.

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