A number in Shikaku gives an area. Factor pairs turn that area into a short list of rectangle dimensions. You do not need advanced mathematics: you are simply looking for two whole numbers whose product equals the clue.
This is a practical tool for solving, not a separate rule. Each candidate still has to contain its clue, avoid other clues and fit with the rest of the board.
Build the list of dimensions
For a clue of 6, multiply 1 × 6 or 2 × 3. Rotating those shapes gives 6 × 1 and 3 × 2. Written as width by height, those are the four different orientations to consider.
| Clue | Dimension pairs before rotation |
|---|---|
| 4 | 1 × 4, 2 × 2 |
| 6 | 1 × 6, 2 × 3 |
| 7 | 1 × 7 |
| 12 | 1 × 12, 2 × 6, 3 × 4 |
A square such as 2 × 2 looks the same when rotated, so it does not add another orientation. A 2 × 3 rectangle does: two cells across and three down is different from three across and two down.
Filter by the board dimensions
Suppose the board has six columns and four rows. A 6 × 1 strip fits horizontally, but a 1 × 6 strip cannot fit vertically. A 2 × 3 and a 3 × 2 region fit dimensionally, although clues or existing rectangles may block them.
For a clue of 12 on that board, a twelve-cell strip is impossible in either direction. A 6 × 2, 3 × 4 or 4 × 3 placement might remain. A 2 × 6 placement does not fit the four-row height.
Being precise about orientation prevents a common shortcut from becoming a mistake: a factor pair fitting one way does not mean it fits both ways.
Prime clues make strips
A prime number has only the positive factor pair 1 and itself. A clue of 7 therefore needs a seven-cell strip. If the grid cannot hold that strip vertically, it must run horizontally.
That does not automatically reveal the strip’s endpoints. On a wider board, the number may have several legal positions within the strip. Look for nearby clues and edges that force where it starts or ends.
A clue of 1, when present, occupies just its own cell. It is a useful boundary for other regions, even though 1 is not a prime number.
Shapes and placements are different questions
Knowing that a clue must be a 2 × 3 rectangle is only half the task. You must also locate it. The clue could sit in any of those six cells.
Imagine sliding a transparent 2 × 3 window over the grid while keeping the clue inside. Discard every position that reaches outside the board, takes another clue or overlaps a confirmed region. If exactly one placement survives, you have a forced move.
Put the method into practice
Pick a clue, list its factor pairs and cross out impossible orientations mentally. Then examine positions. Finally, ask whether the proposed region leaves its neighbors enough space.
Sukto lets you draw the resulting rectangle directly and remove it by tapping an occupied cell if you need to revise. Combine this number-first technique with the space-first approach in our Shikaku strategies guide. If you are still learning the basic geometry, start with how to play Shikaku.
