Discover the world of divisibility in a completely new way! The Number Divider app is a virtual tool that allows you to actively and exploratively investigate division.

With this app you will learn the basics of division with and without remainder and discover divisors of a number.

• Visualize numbers and their divisors by arranging tiles
• Experiment with different arrangements and change the dividers
• Immediately recognize whether a number is divisible
• Save important discoveries in your personal archive
• Customize the display to your needs

task examples

which can be edited with the support of the app:

• Examine the number 8. Change the divisor. What does it mean if the divisor is red? What does it mean if it is green?
• Choose the number 9. Find all its divisors. Then describe how you went about your search and what you discovered.
• Lege die Aufgabe 20 : 5. Nun lege immer ein Plättchen dazu und beobachte, wie sich der Rest verändert. Erkläre!
• Take the number 14 and divide it by 2, 3, 4, 5. Write down your discoveries. What do you notice?
• Untersuche die Teiler der Zahlen 1 bis 10. Stimmt es: Je größer die Zahl ist, desto mehr Teiler hat sie? Begründe, warum die Aussage stimmt oder nicht stimmen kann.
• Examine the divisors of the number 16. Each divisor has a partner. Try divisor pairs with other numbers too. What do you notice about these divisor pairs?
• Examine the numbers 15, 16, 17, 18, 19 and 20 one after the other. Which of these numbers are divisible by 2? Why? Make a guess.
• Examine the numbers 8, 9, and 10. Find all the divisors of each number and compare them.
• Find division problems with remainder 1 (2, 3, 4). How can you do it?
• Examine even and odd numbers and their divisors. What do you notice?
• When you compare the divisors of two numbers, is the larger number always the one with more divisors?
• Take the number 24. Systematically find all the divisors. Think about and explain how you can quickly and safely find all the divisors.
• Finde Zahlen, die nur zwei Teiler haben.
• What does the button with the two arrows do when a division problem is displayed? Why can the numbers be swapped? Why doesn't this work if there is a remainder?
• Exploring prime numbers: Examine the numbers from 10 to 20 for their divisors. Which numbers have exactly two divisors?
• Can a number have only one divisor? Explain your answer.
• Finde Zahlen mit besonders vielen Teilern. Was fällt dir auf?
• Compare the number of divisors for the numbers 12, 24, and 36. What do you notice? Can you find any other numbers with a particularly large number of divisors?
• Common divisor: Examine the numbers 18 and 24. What divisors do both numbers have in common? What is the greatest common divisor?
• Develop a strategy to find the greatest common divisor of two numbers.
• Investigating square numbers: Investigate the square numbers 1, 4, 9, 16, 25. What do you notice about the number of their divisors?
• Examine numbers that are divisible by 3 and write them down. What do you notice about the digits of these numbers? How can you determine whether a number is divisible by 3 without doing any math?
• Choose a number and find all its divisors. Always multiply two divisors together. What do you discover? Explain and justify your discovery.

conception and development

This app was created by Christian Urff in Zusammenarbeit mit Jun.-Prof. Dr. Daniel Walter (Universität Dortmund) entwickelt.