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.

The digit patterns you’ll spot below (multiples of 5 always ending in 0 or 5, multiples of 9 having a digit sum divisible by 9) are early, informal glimpses of a branch of mathematics called modular arithmetic, formally developed by Carl Friedrich Gauss in 1801. Spotting these patterns quickly is more than a party trick — it is exactly the kind of mental shortcut that lets you sanity-check a calculator’s answer at a glance, or catch an error in a spreadsheet before it causes real damage.

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: Find Multiples

Multiples Question