Remainders

Remainders printable worksheet
 

I'm thinking of a number.
My number is both a multiple of $5$ and a multiple of $6$.
What could my number be?
What else could it be?
What is the smallest number it could be?
 

I'm thinking of a number.
My number is a multiple of $4$, $5$ and $6$.
What could my number be?
What else could it be?
What is the smallest number it could be?

The Number Sieve below can be used to explore questions like the ones above and many more. Why not experiment and see what you can discover?
 

Here are some more questions you might like to consider:

I'm thinking of a number that is $1$ more than a multiple of $7$.
My friend is thinking of a number that is $1$ more than a multiple of $4$.
Could we be thinking of the same number?

I'm thinking of a number that is $3$ more than a multiple of $5$.
My friend is thinking of a number that is $8$ more than a multiple of $10$.
Could we be thinking of the same number?

I'm thinking of a number that is $3$ more than a multiple of $6$.
My friend is thinking of a number that is $2$ more than a multiple of $4$.
Could we be thinking of the same number?

Here's a challenging extension:

We know that

Can you find a number with the property that when it is divided by each of the numbers 2 to 10, the remainder is always one less than the number it is has been divided by?
Can you find the smallest number that satisfies this condition?

If you haven't already explored The Remainders Game, why not take a look now?