Step 1 of 4 · Spot the keyword
Three keyword patterns — three different tools. Watch each demo.
12 dots — what row counts work?
6 × 4 rectangle — which square tile fills it?
multiples of 3 and 4 — first place they meet
Step 2 of 4 · Why & how — GCF
A rectangular room is 360 cm by 240 cm. What is the largest square tile that fits evenly into both dimensions?
① Why must the tile divide BOTH sides?
Tap a tile size. A tile only "fits evenly" if it divides 360 AND 240 with no leftover.
50 cm
60 cm
120 cm
200 cm
Pick a tile size above.
② How to find the right size with factor trees
For GCF: take the MIN power of each shared prime
2min(4,3) × 3min(1,2) × 5min(1,1)
= 23 × 3 × 5 = 120
Largest square tile = 120 cm × 120 cm
Step 3 of 4 · Factor riddle
A number has factors 1, 2, 4, 8. What is the smallest such number?
The number must be divisible by every listed factor — the smallest is the largest of them.
N must contain 1, 2, 4, 8 in its factor list
The largest required factor is 8
8 itself has factors 1, 2, 4, 8 ✓ — and 8 is the smallest number that fits
N = 8
Trick: when a riddle gives you a list of factors, the answer is often the largest factor in the list (provided it has all the smaller ones too).