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Multiplication Tables


Multiplication Tool

Every answer takes you to the grid. Pick a question:

Grid

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).

×
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

5 times table

  • 5 × 1 = 5
  • 5 × 2 = 10
  • 5 × 3 = 15
  • 5 × 4 = 20
  • 5 × 5 = 25
  • 5 × 6 = 30
  • 5 × 7 = 35
  • 5 × 8 = 40
  • 5 × 9 = 45
  • 5 × 10 = 50
  • 5 × 11 = 55
  • 5 × 12 = 60

Patterns to explore

Click a card to highlight every matching cell in the grid above.

Perfect squares

The diagonal of the grid — cells where row equals column.

12 matchesClick to highlight
p

Prime products

Cells whose product is itself prime. Only in row 1 and column 1.

10 matchesClick to highlight
2k

Even products

Cells whose product is even. Happens whenever either factor is even.

108 matchesClick to highlight
2k+1

Odd products

Cells whose product is odd. Both factors must be odd.

36 matchesClick to highlight
Σ

Highly composite products

Products that show up in many cells — numbers with the most factor pairs inside the grid.

17 matchesClick to highlight

Properties of multiplication

Why the grid looks the way it does.

Commutative property

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 = 21
1
2
3
4
5
2
4
6
8
10
3
6
9
12
15
4
8
12
16
20
5
10
15
20
25

The diagonal is the squares

Cells 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=25
1

Identity element

Multiplying any number by 1 returns the number unchanged. The first row and first column are the integers themselves, in order.

1 × n = n × 1 = n

Distributive property

a × (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
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