19 times 19 is 361 — with the shortcut, the division facts and a drill to make it stick
19 × 19 = 361. Nobody memorises nineteens; the trick is to go via 20 × 20 and correct, which takes two seconds.
19 × 19 = 361. Said out loud in the way most classrooms say it: Nineteen nineteens are three hundred and sixty-one.
Multiplying is repeated addition, so 19 × 19 is nineteen nineteens added together, or equally nineteen nineteens added together. Both routes land on 361.
The fast way to square a number just under a round one is to go through the round number: 19 × 19 = 20 × 20 − 20 − 19 = 361. Or use the square pattern (20 − 1)² = 400 − 40 + 1 = 361.
361 has a famous home: a full-size Go board is a 19 × 19 grid, so it has 361 points to play on. That is why the number comes up so often in discussions of the game and of computer Go.
Once 19² is solid, the neighbours follow: 18 × 19 is 361 − 19 = 342, and 19 × 20 is 361 + 19 = 380.
Method 1, split 19 into 10 + 9: 19 × 10 = 190 and 19 × 9 = 171. Add them: 190 + 171 = 361.
Method 2, the near-square trick (19 is 1 from 20): Go 1 down and 1 up: 18 × 20 = 360. Then add 1 squared: 360 + 1 = 361.
Nineteen is one short of twenty. Twenty nineteens are 380, take one nineteen back and you are left with 361.
19 × 19 is a square number: 361 is what you get when 19 is multiplied by itself, which is why the square root of 361 is 19.
Both factors are odd, so the answer has to be odd as well. 361 is odd, which rules out a whole class of slips.
19 × 19 = 361 and 361 ÷ 19 = 19 are one fact read in different directions. The facts either side — 19 × 18 = 342, 19 × 20 = 380, 18 × 19 = 342, 20 × 19 = 380 — are the answers people most often give by mistake when rushing, and each is just one nineteen away from 361.
19 × 19 sits in two lists at once: row 19 of the nineteen times table, and the nineteenth square number. The highlighted row is 361.
| × | 19 times table | Square numbers |
|---|---|---|
| 1 | 19 × 1 = 19 | 1 × 1 = 1 |
| 2 | 19 × 2 = 38 | 2 × 2 = 4 |
| 3 | 19 × 3 = 57 | 3 × 3 = 9 |
| 4 | 19 × 4 = 76 | 4 × 4 = 16 |
| 5 | 19 × 5 = 95 | 5 × 5 = 25 |
| 6 | 19 × 6 = 114 | 6 × 6 = 36 |
| 7 | 19 × 7 = 133 | 7 × 7 = 49 |
| 8 | 19 × 8 = 152 | 8 × 8 = 64 |
| 9 | 19 × 9 = 171 | 9 × 9 = 81 |
| 10 | 19 × 10 = 190 | 10 × 10 = 100 |
| 11 | 19 × 11 = 209 | 11 × 11 = 121 |
| 12 | 19 × 12 = 228 | 12 × 12 = 144 |
| 13 | 19 × 13 = 247 | 13 × 13 = 169 |
| 14 | 19 × 14 = 266 | 14 × 14 = 196 |
| 15 | 19 × 15 = 285 | 15 × 15 = 225 |
| 16 | 19 × 16 = 304 | 16 × 16 = 256 |
| 17 | 19 × 17 = 323 | 17 × 17 = 289 |
| 18 | 19 × 18 = 342 | 18 × 18 = 324 |
| 19 | 19 × 19 = 361 | 19 × 19 = 361 |
These are the facts one step away from 19 × 19 in the grid, and the answers people give by mistake when rushing. The last column shows how far each lands from 361; tap a fact to open it or its times table.
| Fact | Answer | Compared with 361 |
|---|---|---|
| 19 × 18 | 342 | 19 less |
| 19 × 20 | 380 | 19 more |
| 18 × 19 | 342 | 19 less |
| 20 × 19 | 380 | 19 more |
| 18 × 20 | 360 | 1 less |
| 20 × 18 | 360 | 1 less |
Use the drill on this page for a 60-second quiz on 19 × 19 and its neighbours, read the 19 times table in full, or play the arcade game until the answer comes without counting.
19 times 19 is 361. In words, nineteen nineteens are three hundred and sixty-one.
361 ÷ 19 = 19, because 19 × 19 = 361.
Method 1, split 19 into 10 + 9: 19 × 10 = 190 and 19 × 9 = 171. Add them: 190 + 171 = 361. Method 2, the near-square trick (19 is 1 from 20): Go 1 down and 1 up: 18 × 20 = 360. Then add 1 squared: 360 + 1 = 361.
361 ÷ 19 = 19. 361 is 19 squared, so dividing it by 19 gives 19 straight back.
Every times table from 1 to 20 is written out on the times tables page, with a drill for any row, and the full grid is on the multiplication chart.