Factor Merge
Factor Merge is a calm number game on a four-by-four board. Three target cards sit above it, and the board holds numbered tiles. Tap one tile, then tap another: the second tile becomes their product, and the first tile's cell empties. The tiles do not have to be next to each other, because position is not the skill. Factors are.
There is one rule, and it is the whole game. A merge is allowed only if the product is a factor of at least one open target. Try 6 × 7 with targets 24, 36 and 60 and the move is refused, with the reason: 42 is not a factor of 24, 36 or 60. Nothing else happens, but the refusal is counted. When a tile equals a target, that target is made. The tile and the card clear, your score goes up by one, a new target is dealt, and the game shows what the number was made of, such as 24 = 4 × 6.
After each allowed merge, new tiles arrive. On Grades 3–5 two come: one is a factor of an open target, and the other is any number from 2 to 9, so it may fit no target at all. On Grades 6–8 one prime comes, and a second when you make a target, and each is a factor of an open target. A tile that was useful when it landed can stop being useful once its target has been made. Tiles pile up that no target needs any more, and the run ends when no two tiles on the board can be merged. Three times a run you can clear a tile to throw one away, and no tile arrives after a clear. There is no clock and there are no lives. Choose Grades 3–5 for multiplication facts, with tiles from 2 to 9, or Grades 6–8 for prime factors, GCF and LCM, with tiles that are the primes 2, 3, 5 and 7. The page remembers the level you chose last, and your best score for each level is saved on this device.
Frequently asked questions
How do you play Factor Merge?
Tap a tile to pick it, then tap another tile to multiply the two. The second tile becomes the product and the first tile's cell empties. Tap the picked tile again to put it back. On a keyboard, the arrow keys move between tiles, Space or Enter picks one, and Esc puts a picked tile back. The merge goes through only if the product is a factor of at least one of the three targets above the board; otherwise it is refused and the page says why.
Why was my merge refused?
Because the product does not divide any open target. With targets 24, 36 and 60, a 2 and a 3 can be merged, since 6 goes into all three. A 6 and a 7 cannot, since 42 goes into none of them. A refused merge changes nothing on the board, but it is counted and shown on the end screen. Asking "what times this tile gives a factor of a target?" before you tap is the skill the game is for.
What is the difference between Grades 3–5 and Grades 6–8?
Grades 3–5 uses the multiplication facts. The tiles run from 2 to 9, and every target is a product of two of those numbers between 12 and 81, such as 24, 36 or 56. Grades 6–8 uses primes. The tiles are only 2, 3, 5 and 7, and the targets are numbers from 12 to 120 whose prime factors are only those four. A target of 14 takes one merge, 12 takes two, and 60 takes three, and when you make it the game shows 60 = 2 × 2 × 3 × 5.
What do the LCM and GCF cards ask for?
On Grades 6–8 a card says Make 60, or the LCM of two numbers, or the GCF of two numbers. About half are Make cards, and a quarter each are LCM and GCF. For an LCM or GCF card, work out the number first: the LCM of 4 and 6 is 12, and the GCF of 36 and 48 is 12. Then build that number from the tiles. The LCM cards use numbers from 2 to 12, except 11, and the GCF cards use numbers up to 100.
How does a run end, and how is it scored?
A run ends when no two tiles on the board can be merged, which usually means the tiles left over no longer fit any target. The score is the number of targets made, and the end screen also counts the merges you were refused. Every 10 targets made, the smallest target the game deals goes up, to 24, then 36, then 48. The end screen links to worksheets that practise the same ideas: factors and multiples for Grades 3–5, and prime numbers, GCF and LCM for Grades 6–8.