The worksheets themselves are in German – just as in class. The editor is only available in German so far.
Factors & multiples – worksheets to print
Find factors and multiples, use divisibility rules, split numbers into prime factors, find the HCF and LCM.
- Choose the number of tasks and the difficulty yourself
- With an answer sheet and, if you like, a QR code to the answers
- At three levels (★ to ★★★) and as group A and B
- As a single worksheet or as a task on a mixed worksheet
Factors & multiples: explained simply
Explore which numbers divide another number without a remainder, and which numbers appear when you multiply it repeatedly by whole numbers.
How to work it out
- A factor divides a number exactly. Multiples come from ·1, ·2, ·3 and so on; these lists start with the first positive multiple.
- Divisible by 2: the last digit is even; by 5: it ends in 0 or 5; by 10: it ends in 0. For 3 or 9, the digit sum must be divisible by 3 or 9. For 4, the last two digits must form a number divisible by 4.
An example, step by step
Find all the factors of 12.
- Find multiplication pairs: 1 · 12 = 12, 2 · 6 = 12 and 3 · 4 = 12.
- Collect both numbers from every pair.
- In order, the factors are 1, 2, 3, 4, 6 and 12.
Understand other variations
Prime factors
Keep splitting until only primes remain: 12 = 2 · 6 = 2 · 2 · 3. A prime number has exactly two positive factors: 1 and itself.
Highest common factor and lowest common multiple
The highest common factor of 12 and 18 is 6. Their lowest common positive multiple is 36: the lists 12, 24, 36 … and 18, 36 … first meet there. German worksheets use ggT and kgV for these two quantities.
More divisibility rules
Divisible by 6 means divisible by both 2 and 3. For 8, check the last three digits. For 25, check for endings 00, 25, 50 or 75.
Your turn
Is 42 divisible by 3? Name the first three positive multiples of 7.
Show the answer and method
Yes: 4 + 2 = 6 is divisible by 3. The multiples are 7, 14 and 21.
Ready-made worksheets: Factors & multiples
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