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## 'Sieve of Eratosthenes' printed from http://nrich.maths.org/

You will need to print one copy of this

2-100 master grid,
and a copy of this sheet of

smaller
grids.

On the first small grid, shade in
all the multiples of 2 except 2.
- What do you notice? Can you explain what you see?
- Now update the master grid, by crossing out the multiples
of 2 except 2.

On the second small grid, shade in
all the multiples of 3 except 3.
- What do you notice? Can you explain what you see?
- Before you update the master grid, can you predict what will happen?
Will you cross out any numbers that are already crossed
out? If so, which ones?
- Now update the master grid, by crossing out the multiples of 3
except 3. Can you explain why some numbers have
been crossed out twice and others only once?

Use the next four small grids to
explore what happens for multiples of 4, 5, 6 and 7.
- Before you shade in the multiples of each number (but not the
number itself), try to predict what patterns might
emerge.
- After you have shaded in the multiples, try to explain the patterns you've
found.
- Before you update the master grid, try to predict what will
happen. Will you cross out any numbers that are already
crossed out? If so, which ones?
- After you have updated the master grid, try to explain why some numbers have
been crossed out again and others haven't.

Now look at the master grid.
What is special about the numbers that you haven't crossed
out?

What would change on the master
grid if you were to cross out multiples of larger
numbers?
We're used to working with grids
with ten columns, but you might find an interesting result if you
use this six-column grid
instead. Can you
predict

what you will see?
Try it!
Final challenge

Imagine you want to find all the
prime numbers up to 400.
You could do this by crossing out
multiples in a 2-400 number grid.
Which multiples will you choose to
cross out?
How can you be sure that you are
left with the primes?
(Here is a 2-400 number grid
if you want to try
it.)

With thanks to Vicky Neale
who created this task in collaboration with NRICH.