Divisors and multiples
This page was translated from German with AI. It has not been checked by a native speaker. Original page in German
The video
In the video we share a pizza. The children's pieces are orange and pink in turn; what is left over is dark.
Contents of the video
- 0:00 Sharing a pizza fairly
- 0:24 Something is left over
- 0:40 Divisors
- 1:10 Multiples
- 1:37 Divisible by two, five and ten
- 2:13 Divisible by three and nine
- 2:44 Careful, mistake!
- 3:04 Try it yourself
- 3:40 Summary
The most important points
Divisor (der Teiler)
\( 3 \) is a divisor of \( 12 \), because \( 12 : 3 = 4 \) has no remainder. \( 5 \) is not a divisor of \( 12 \). Look for the divisors in pairs: \( 1 \cdot 12 \), \( 2 \cdot 6 \), \( 3 \cdot 4 \).
Multiples (die Vielfachen)
The multiples of \( 4 \) are the four times table: 4, 8, 12, 16, 20, … \( 12 \) is a multiple of \( 4 \), and \( 4 \) is a divisor of \( 12 \).
Divisibility rules
By 2: last digit 0, 2, 4, 6, 8. By 5: last digit 0 or 5. By 10: last digit 0. By 4: the last two digits are divisible by 4, for example 532. By 3 and by 9: the digit sum (die Quersumme, all digits added) is divisible by 3 or 9.
The worksheet
Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.
📄 Open worksheet (PDF, German)
Show the worksheet solutions
Try it yourself
Task
a) Find all divisors of 18. b) Is 135 divisible by 2, by 3 and by 5?
Show solution
a) 1, 2, 3, 6, 9, 18 (\( 1 \cdot 18 \), \( 2 \cdot 9 \), \( 3 \cdot 6 \)) b) not by 2, but by 5 (last digit 5) and by 3 (digit sum 9)
Keep learning with a language model
You are my maths teacher. I am learning German as a second language. Our topic: divisors and multiples (Teiler und Vielfache: pairs of divisors, divisibility rules, digit sum). Give me five short tasks, one after the other. Always wait for my answer, then explain briefly. Write in simple German and put an English translation in brackets after each sentence.
How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.
The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.
The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.