3 times table, the pattern behind the threes.

The 3 times table is the list of multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 up to 3 × 12. Its best trick is in the digits, because adding the digits of any answer gives 3, 6 or 9. The tool above shows the table, hides answers for a self-test, runs a scored quiz that explains every wrong answer, and prints a chart or sheet.

How to use the 3 times table tool

1. Click Table to see the facts, the patterns for this number and the skip counting line. Go up to shows the table to 10, 12, 15 or 20.
2. Tick Hide the answers to test yourself. Tap a row to reveal its answer.
3. Click Practice quiz, then Start the quiz. Type each answer and press Enter. A wrong answer shows a quick way to work it out.
4. Under Quiz questions choose 10, 20, 30 or every fact once. Tick Ask both ways round or Include division to make the quiz harder.
5. At the end, read your score and click Practise the missed ones to go over only the facts you got wrong.
6. Use Print table for a clean sheet, Print practice sheet for a blank one, Copy table to paste the list, and Copy link to share your settings.

The 3 times table, 1 to 12

The digit sum pattern

Add the digits of each answer. 12 gives 1 + 2 = 3, 15 gives 6, 18 gives 9, 21 gives 3, 24 gives 6, 27 gives 9, 30 gives 3, 33 gives 6, 36 gives 9. The sums repeat 3, 6, 9. This gives you a test for divisibility by 3: a number is in the 3 times table if its digits add up to a number in the table. 249 gives 2 + 4 + 9 = 15, which is in the table, so 249 = 3 × 83.

Double and add one more

Three is 2 + 1. For 3 × 8, double 8 to get 16, then add 8 for 24. For 3 × 12, double 12 to get 24 and add 12 for 36. If you know the 2 times table, you can find any fact in the 3 table with one more addition.

Odd, even, odd, even

Because 3 is odd, the answers alternate: 3 is odd, 6 is even, 9 is odd, 12 is even. The ones digit goes 3, 6, 9, 2, 5, 8, 1, 4, 7, 0 and uses every digit once before it repeats. That is one reason the table can feel slippery: the ones digit never settles into a short cycle like it does in the 2, 4, 5 and 6 tables.

From 3 to 6 and 9

The 6 table is the 3 table doubled: 3 × 7 = 21 and 6 × 7 = 42. The 9 table is the 3 table tripled: 3 × 4 = 12 and 9 × 4 = 36. So the 3 table is worth learning well first.

Worked examples

• Trios. 7 groups of 3 children are 3 × 7 = 21 children.
• Digit sum test. Is 135 in the table? 1 + 3 + 5 = 9, so yes: 135 = 3 × 45.
• Division. 27 ÷ 3 = 9, because 3 × 9 = 27.
• Missing number. 3 × ? = 24. The answer is 8.
• Past 12. 3 × 14 = 42 and 3 × 20 = 60.

Beyond 12: 3 × 13 to 3 × 20

Set Go up to to 20 and the tool shows these as well. For any of them, split the number: 3 × 13 is 3 × 10 plus 3 × 3, which is 30 + 9 = 39.

Common mistakes

• Confusing 3 × 7 = 21 with 3 × 8 = 24, and 3 × 9 = 27 with 3 × 12 = 36.
• Forgetting the carry in the doubling method: double 9 is 18, plus 9 is 27, not 25.
• Forgetting that 3 × 11 = 33 and 3 × 12 = 36 are in the table too.

A way to learn it

Learn 3, 6, 9, 12, 15 first, then 18 to 30. The last two, 33 and 36, are 3 × 11 (repeat the 3) and 3 × 12 (a dozen threes). Use the digit sum card above to check each answer as you go.

Next, try the 4 times table, or go back to the 2 times table. To see every table in one grid, use the times tables chart. To make your own cards, try the flashcard maker.