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On the first small grid, shade in all the multiples of 2 except 2.
On the second small grid, shade in all the multiples of 3 except 3.
Use the next four small grids to explore what happens for multiples of 4, 5, 6 and 7.
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!
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.)
Imagine you want to find all the prime numbers up to 1000 by crossing out multiples in a 2-1000 number grid.
Which number will you cross out last?
A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either its first or its last digit. Find all strange numbers.