Interactive Math Reference

Multiplication Grid (1–12)

Click any cell to lock row and column coordinates. Use the filters to reveal hidden patterns — square numbers, prime products, even/odd distributions, and multiples.

Highlight:
Multiples of:
× 1 2 3 4 5 6 7 8 9 10 11 12
1 1 2 3 4 5 6 7 8 9 10 11 12
2 2 4 6 8 10 12 14 16 18 20 22 24
3 3 6 9 12 15 18 21 24 27 30 33 36
4 4 8 12 16 20 24 28 32 36 40 44 48
5 5 10 15 20 25 30 35 40 45 50 55 60
6 6 12 18 24 30 36 42 48 54 60 66 72
7 7 14 21 28 35 42 49 56 63 70 77 84
8 8 16 24 32 40 48 56 64 72 80 88 96
9 9 18 27 36 45 54 63 72 81 90 99 108
10 10 20 30 40 50 60 70 80 90 100 110 120
11 11 22 33 44 55 66 77 88 99 110 121 132
12 12 24 36 48 60 72 84 96 108 120 132 144

Click any cell in the grid to inspect its factors and arithmetic properties →

Patterns to spot

What's hiding in the grid?

Click any card below to instantly highlight its pattern in the table above.

Square numbers

The diagonal from top-left to bottom-right (1, 4, 9, 16 … 144) are all square numbers — they appear when a number multiplies itself.

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Prime products

Only 5 products in the entire grid are prime: 2, 3, 5, 7, and 11. A prime only appears when one of its factors is 1 — so it only lives in row 1 or column 1.

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Even vs odd

75% of products in the grid are even! Only when both factors are odd (e.g. 3×5, 7×9) do you get an odd result — just 36 out of 144 cells.

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Mirror symmetry

The grid is perfectly symmetrical along the diagonal — 3×7 = 7×3 = 21. This is the commutative property. You only need to learn half the facts!

Spot it along the diagonal

Largest product

12 × 12 = 144 is the largest value in the grid. Look across each row to see how rapidly products grow compared to smaller tables.

Bottom-right corner

Multiples of 12

12 has the most factors of any number up to 12 (1, 2, 3, 4, 6, 12) — which is why base-12 is used for clocks, hours, and dozens.

Click to highlight →