Multiplication Table 1–20

Interactive times table chart for quick reference

× 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
4 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80
5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
6 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120
7 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140
8 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 128 136 144 152 160
9 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 162 171 180
10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
11 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198 209 220
12 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240
13 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 208 221 234 247 260
14 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 224 238 252 266 280
15 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300
16 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256 272 288 304 320
17 17 34 51 68 85 102 119 136 153 170 187 204 221 238 255 272 289 306 323 340
18 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360
19 19 38 57 76 95 114 133 152 171 190 209 228 247 266 285 304 323 342 361 380
20 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400

What is a Multiplication Table?

A multiplication table (or times table) is a mathematical reference that shows the products of pairs of numbers. The table above shows all products of numbers from 1 to 20, giving 400 products ranging from 1 × 1 = 1 to 20 × 20 = 400. To find any product, locate one factor in the row header and the other in the column header — the intersection gives the result.

Learning Multiplication

Memorizing the multiplication table is a fundamental skill in elementary mathematics education. Most curricula require students to learn tables up to 10 × 10 or 12 × 12. Strategies for learning include: skip counting (2, 4, 6, 8...), patterns (the 9s table: digits always sum to 9), commutativity (knowing 7 × 8 means you also know 8 × 7), and anchor facts (using known products to derive unknown ones).

The commutative property (a × b = b × a) means the table is symmetric along the diagonal — you only need to memorize roughly half of all products. The products along the main diagonal (1, 4, 9, 16, 25...) are the perfect squares.

Patterns in the Table

The multiplication table is rich with mathematical patterns. The 1s row/column contains the identity: n × 1 = n. The 2s row/column doubles each number. The 5s column alternates between ending in 0 and 5. The 9s pattern: in the products 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, the tens digit increases by 1 while the ones digit decreases by 1, and the digits always sum to 9.

The 10s row/column simply appends a zero. Even rows contain only even products; odd rows alternate between odd and even products. The distribution of prime numbers in the table is notable: primes only appear in the 1s row/column (since primes have no factors other than 1 and themselves).

Historical Context

Multiplication tables have been used for thousands of years. The oldest known tables date to ancient Babylon (circa 2000 BC), written on clay tablets in base 60. The Chinese had multiplication tables carved in bamboo strips by 305 BC. The Pythagorean table (named after Pythagoras, though not invented by him) is the standard format used today. In the Middle Ages, multiplication tables were essential tools for merchants and scholars.

Beyond Basic Multiplication

Understanding the multiplication table leads to deeper mathematical concepts: factorization (which numbers appear as products and how), divisibility rules, common multiples, and greatest common divisors. The table also connects to area calculations in geometry (the area of a rectangle with integer sides is their product) and to scaling in everyday life.