Check the belt
A factor arrangement leaves no tiles on the leftovers belt.
Factor Factory
Arrange a conserved batch of tiles into equal rows and inspect leftovers.
Grades 3–5 · Math
Your goal
Pack 12 tiles into 3 equal rows with no leftovers. Discover its factor partner.
Reduced motion is on. The controls still update the scene.
5 rows of 2 tiles use 10 of 12 tiles, leaving 2. 5 is not a factor because the tiles do not fit equally.
All tiles are conserved between the rectangular pack and the leftovers belt. Tile size adapts to keep large arrays visible. A complete factor pair always multiplies back to the batch total.
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Learn with Factor Factory
Factor Factory connects multiplication and division with a batch of equal tiles. Change the number of rows to repack the tiles, then inspect how many fit in each row and how many remain on the leftovers belt. A complete rectangle identifies a genuine factor pair because every tile belongs to an equal row. Nine goals ask upper elementary students to construct arrays for different batch sizes. The feedback distinguishes complete packs from incomplete ones, helping learners explain divisibility and verify each factor pair by multiplying back to the total.
What to look for
Read both dimensions
Rows multiplied by tiles per row gives the packed total.
Keep every tile
Packed tiles plus leftovers must always equal the batch size.
For teachers and curious learners
Identify factor pairs through complete rectangular arrays. Ask students to predict what will happen, change one setting, and explain what they observe. Learn gives a starting point. Practice and Challenge offer new goals with the same scene.
Exact whole-tile grouping uses between one and twelve rows with integer quotient and remainder. All tiles are conserved. Tile sizes adapt for visibility, so the printed counts define the quantities.