A Conversation Piece
1 out of 3
Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?
Problem
Getting Started
$1$ is not a prime number!
Use a calculator and be methodical.
Student Solutions
Caroline from Tattingstone and Douglas from Burgoyne Middle School both began by listing the first ten prime numbers:
2,3,5,7,11,13,17,19,23,29.
They then proceeded in the same way:
6469693230/2=3234846615
3234846615/3=1078282205
1078282205/5=215656441
215656441/7=30808063
30808063/11=2800733
2800733/13=215441
215441/17=12673
12673/19=667
667/23=29
29/29=1
And the answer they arrived at was 1!
Clearly worked out - well done.
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 offers a lot of practice of division as well as revision of ideas about prime numbers in a situation in which children want to get to the answer - much more fun than a page of calculations but just as much practice. It requires a calculator unless someone really relishes long division!
Key questions
Possible extension
Learners who find it easy could be encouraged to invent their own similar problems which will give them practice with multiplication as well as division.