Every answer takes you to the grid. Pick a question:
The cell at row a, column b shows a × b. The diagonal holds perfect squares; the grid is symmetric about it (a × b = b × a).
Click a card to highlight every matching cell in the grid above.
The diagonal of the grid — cells where row equals column.
Cells whose product is itself prime. Only in row 1 and column 1.
Cells whose product is even. Happens whenever either factor is even.
Cells whose product is odd. Both factors must be odd.
Products that show up in many cells — numbers with the most factor pairs inside the grid.
Why the grid looks the way it does.
a × b = b × a. The grid is a mirror image of itself across the diagonal — every cell has a twin on the other side.
3 × 7 = 21 · 7 × 3 = 21Cells where row equals column are perfect squares: 1, 4, 9, 16, 25… See the full perfect squares page.
1²=1, 2²=4, 3²=9, 4²=16, 5²=25Multiplying any number by 1 returns the number unchanged. The first row and first column are the integers themselves, in order.
1 × n = n × 1 = na × (b + c) = a × b + a × c. The classic mental-math trick: break one factor into a sum.
7 × 12 = 7 × 10 + 7 × 2 = 70 + 14 = 84