Finding Multiples – Lists, Patterns and Checks
Finding multiples is straightforward: multiply the number by 1, 2, 3, and so on. But there are faster techniques and patterns worth knowing.
Method 1 – Direct Multiplication
First 10 multiples of 6
6×1=6 6×2=12 6×3=18 6×4=24 6×5=30 6×6=36 6×7=42 6×8=48 6×9=54 6×10=60
Method 2 – Skip Counting
Start at the number and repeatedly add the number. Useful for quick mental work.
Multiples of 9 by skip counting: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90...
Method 3 – Divisibility Check
To check if a number is a multiple, divide it by the original number. If the remainder is 0, it is a multiple.
Is 126 a multiple of 7?
126 ÷ 7 = 18 exactly. Remainder = 0. Yes, 126 is a multiple of 7.
Patterns to Spot
| Number | Pattern in Multiples |
|---|---|
| 2 | Always even — ends in 0, 2, 4, 6, 8 |
| 5 | Always ends in 0 or 5 |
| 9 | Digit sum always divisible by 9 |
| 10 | Always ends in 0 |
| 11 | Alternating digit difference = 0 |
Finding Large Multiples
Find the 25th multiple of 13
25th multiple = 13 × 25 = 325
Which multiple of 8 is closest to 100?
100 ÷ 8 = 12.5. So 12th multiple = 96; 13th = 104. Closest = 96.
Key Takeaways
- To find multiples, multiply by 1, 2, 3, ... or skip count.
- To test if N is a multiple of M, check N ÷ M has remainder 0.
- Many numbers have recognisable digit patterns in their multiples.
- There is no largest multiple — they continue infinitely.
Practice Questions
- List the first 8 multiples of 13.
- What is the 20th multiple of 4?
- Is 252 a multiple of 6? Show your working.
- List all multiples of 7 between 50 and 100.
- Find the largest multiple of 9 that is less than 200.