Factor Pair Tiles Game

How to Play Factor Pair Tiles

Find every different whole-number factor pair of the displayed area. Choose one tile for the rectangle’s length and a separate tile for its width. The two side lengths must multiply to the exact target area. Check rectangle records a valid new pair. After verification, the tiles return to the tray so you can construct another rectangle for the same area.

The available tray includes every needed side length and some distractors. You cannot use the same physical tile twice in one rectangle. Square areas include two separate tiles for their repeated square-root factor, allowing a square to be built legally. Selecting a chosen tile again, or selecting its side box, removes that side so you can try another value.

Rotations are the same factor pair. A rectangle with length 3 and width 8 is equivalent to one with length 8 and width 3; it is recorded only once. The found-pair list shows your progress, but you must work out which pairs are missing. The round finishes when all different unordered pairs have been correctly recorded.

Worked Example: Rectangles with Area 24

For area 24, the complete factor pairs are 1 × 24, 2 × 12, 3 × 8 and 4 × 6. Each product equals 24, even though the rectangle shapes differ. The next integers, 5 and 6, do not introduce a new smaller-side pair: 5 does not divide 24, and 6 × 4 is the rotation of the already recorded 4 × 6.

To find every pair systematically, test possible smaller side lengths through the square root of the area. When an integer a divides the area exactly, the matching width is area ÷ a. Stopping after the square root prevents you from counting rotated rectangles again. A perfect square, such as 36, includes the pair 6 × 6 once.

The diagram scales a rectangle uniformly to fit the board while preserving its side-length ratio. Small rectangles also show unit divisions. Very long, thin rectangles are shown with an outline and exact side labels, so rely on the numeric dimensions when counting units would be impractical. A rejected choice displays its actual product and compares it with the required area.

Factor Practice, Levels and Records

Easy uses target areas from 12 to 24. Normal introduces areas up to 60, and Hard reaches 120 with more factor relationships to inspect. The number of factor pairs varies by target, so follow the Found count rather than expecting an identical number of rectangles each round. This combines multiplication, exact division and area reasoning in one task.

All tile and side controls work with touch, Tab, Enter and Space; dragging is not required. Undo restores a previous selection or recorded pair and marks assistance. A hint gives an unrecorded pair and its product. Daily and Practice puzzles save separately for every level, including unfinished side selections and the pairs already verified.

Incorrect checks reduce the possible score by five points and each hint by fifteen, with a minimum completed score of ten. There is no timer. Hints and Undo mark the round assisted, so its score does not replace an unaided best. A completed puzzle is counted once, even after reload or a daily restart. Browser records are local, and the game remains usable when browser saving is unavailable.

Frequently Asked Questions

Does rotating a rectangle create another pair?

No. Length × width and width × length represent the same unordered factor pair.

Can I use one tile for both sides?

No. Use two separate tiles. Square areas include duplicate square-root tiles for the square pair.

Do tiles disappear after a correct rectangle?

No. They return to the tray after verification; the limited tile selection applies to each individual rectangle.