Divide It Out
3 out of 3
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Problem
Getting Started
What is the lowest number which divides exactly by all the numbers from $2$ to $10$?
Student Solutions
Briony explained her way of working this out very well.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
This problem requires logical thinking about factors and much multiplication! Learners must first find out what is the lowest number which divides exactly by all the numbers from $2$ to $10$ and then decide how this helps to answer the question asked. A calculator could be useful for checking.
Key questions
Possible extension
Learners could find the lowest number which always leaves a remainder of $1$ when divided by any of the numbers from $2$ to $12$, or $2$ to $20$, etc.
Possible support
Suggest starting by finding the lowest number which divides exactly by all the numbers from $2$ to $6$. A calculator might be very helpful.