A Conversation Piece
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?
Age
7 to 11
Challenge level
Problem
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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
A Conversation Piece
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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
Have you made a list of the first ten prime numbers?
Remember that $1$ is not a prime number.
Which number are you going to divide by first?
How will you know whether you have divided by that number already?