Illuminations: Factorize

Factorize
With this activity, you can visually explore the concept of factors by creating rectangular arrays with an area equal to the product of the factors.

Instructions
 
In Automatic Number mode, numbers will be randomly selected for you. Or, you can enter any number from 1 to 50 in the Use Your Own Number box.

In the grid, create rectangles whose areas are equal to the given number. Then, enter the factorizations in the form __ × __. (Use either x or * for the multiplication symbol.) The rectangles and factorizations are color‑coded so that the color of the rectangle matches the highlight color of the factorization box.

Click New Number to find the factorizations for a different number.

Exploration
 
Click Use Your Own Number and enter 25 in the box. How many different factorizations does 25 have?
  • Which of the numbers 1‑49 has the most factorizations? Which has the least factorizations?
  • What kind of numbers have only one factorization?

  

NCTM Resources

Principles and Standards for School Mathematics
National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
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