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Prime numbers

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

A pizza with 7 pieces can only be shared fairly between 1 or 7 children. Numbers like 7 are called prime numbers. You learn how to find them and how to split numbers into primes.
📄 Open worksheet (PDF, German)

The video

In the video we cross out the numbers up to 30 until only the prime numbers are left. Prime numbers have a green frame.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Seven pieces
  2. 0:18 Prime numbers
  3. 0:41 Finding prime numbers
  4. 1:13 Prime factorisation
  5. 1:40 Careful, mistake!
  6. 2:04 Try it yourself
  7. 2:37 Summary

The most important points

Prime number (die Primzahl)

A prime number has exactly two divisors: \( 1 \) and the number itself. Prime numbers: 2, 3, 5, 7, 11, 13, … \( 1 \) is not a prime number, it has only one divisor.

12 has six divisors: not a prime number.
12 has six divisors: not a prime number.

How to find all prime numbers up to 30: cross out 1. Cross out all multiples of 2, then of 3 and of 5. What is left: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

The sieve up to 30: the prime numbers are green.
The sieve up to 30: the prime numbers are green.

Prime factorisation (die Primfaktorzerlegung)

Split the number until only prime numbers are left: \( 60 = 6 \cdot 10 = 2 \cdot 2 \cdot 3 \cdot 5 = 2^2 \cdot 3 \cdot 5 \). A factor tree (der Faktorbaum) helps. Careful: not every odd number is a prime number, for example \( 9 = 3 \cdot 3 \).

Two factor trees for 60: at the end there are the same prime numbers.
Two factor trees for 60: at the end there are the same prime numbers.

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)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
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Show the worksheet solutions
The worksheet – Page 4
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Try it yourself

Task

a) Is 21 a prime number? b) Write 36 as a product of prime factors.

Show solution

a) No, \( 21 = 3 \cdot 7 \). b) \( 36 = 2 \cdot 2 \cdot 3 \cdot 3 \)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: prime numbers and prime factorisation (Primzahlen, Faktorbaum). 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.