The 3, 6 and 9 Times Tables

Three tables, lots of patterns

The 3, 6 and 9 times tables are full of neat shortcuts. Once you spot the patterns, you will not need to memorise them one fact at a time. Make sure you are comfortable with Doubling and Halving first, because doubling is one of our main tools here.

The 3 times table

Start by counting up in 3s: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30...

A handy check (the digit-sum trick): a number is in the 3 times table if the sum of its digits is a multiple of 3.

• Is 24 a multiple of 3? 2 + 4 = 6, and 6 is in the 3s. Yes (24 = 3 × 8).
• Is 25 a multiple of 3? 2 + 5 = 7, not a multiple of 3. No.

The 6 times table: double the 3s

Because 6 is double 3, the 6 times table is just the 3 times table doubled.

Example — 6 × 7:

1. Find 3 × 7 = 21.
2. Double it: 21 × 2 = 42.
3. So 6 × 7 = 42.

This means once you know your 3s, you almost know your 6s too.

The 9 times table: two great tricks

The 9s look hard but hide two lovely patterns.

Trick 1 — the digit-sum. In every 9 times answer, the two digits add up to 9:

• 9 × 2 = 18 → 1 + 8 = 9
• 9 × 5 = 45 → 4 + 5 = 9
• 9 × 8 = 72 → 7 + 2 = 9

Trick 2 — the finger method. Hold up all ten fingers. To work out 9 × 4, bend down your 4th finger from the left.

• Fingers to the left of the bent one = the tens digit (3 fingers → 30).
• Fingers to the right = the units digit (6 fingers → 6).
• So 9 × 4 = 36.

This works for every fact from 9 × 1 up to 9 × 10. The why behind it: each step adds 9, which raises the tens by one and lowers the units by one — exactly what your fingers show.

The three tables together

×	3s	6s	9s
1	3	6	9
2	6	12	18
3	9	18	27
4	12	24	36
5	15	30	45
6	18	36	54
7	21	42	63
8	24	48	72
9	27	54	81
10	30	60	90
11	33	66	99
12	36	72	108

Look across each row: the 6s are double the 3s, and the 9s are the 3s tripled.

Worked example

A tricycle has 3 wheels. A bus tour uses 6 tricycles. How many wheels altogether, and how does that compare to 9 tricycles?

1. 6 tricycles → 6 × 3 = 18 wheels (or 3 × 6, the swap).
2. 9 tricycles → 9 × 3 = 27 wheels. Check the 9s pattern: 2 + 7 = 9. ✔
3. So 9 tricycles have 9 more wheels than 6 tricycles (27 − 18 = 9), one extra group of 3 per added tricycle... actually three per tricycle, nine in total. The patterns agree.

Try it yourself

• Count up in 3s to 36, then double each number to make the 6 times table.
• Use the finger trick to say all the 9 times facts in order.
• Digit-sum check: is 51 a multiple of 3? Is 48 a multiple of 9?

(Answers: 5 + 1 = 6 → yes, 51 = 3 × 17; 4 + 8 = 12, not 9, so 48 is not in the 9 times table.)

Where this leads

These patterns power the Divisibility Rules you will meet later, and they speed up your overall Times Tables recall. Spotting patterns instead of memorising blindly is a skill that pays off in every part of maths.