$44$ and $44444$ are numbers where every digit is $4$. Explain why any positive integer where every digit is $4$ must be divisible by $2$ and $4$.

Here are two facts about a number:

Every digit is $4$.

It is divisible by $5$.

Explain why this is impossible.

Here are two facts about a number:

Every digit is $4$.

It is divisible by $3$.

Find a number with both these properties.

Here are two facts about a number:

Every digit is $4$.

It is divisible by $3$.

Is there more than one possible number? Give a reason for your answer.

Here are two facts about a number:

Every digit is $4$.

It is divisible by $11$.

Find a number with both these properties.

Here are two facts about a number:

Every digit is $4$.

It is divisible by $11$.

Is there more than one possible number? Give a reason for your answer.

$2\times 4=8$

Look at this statement: A number is divisible by $8$ when it is divisible by $2$ and by $4$. Do you think the statement is correct? Give evidence to justify your answer.

$2\times 5=10$

Look at this statement: A number is divisible by $10$ when it is divisible by $2$ and by $5$. Do you think the statement is correct? Give evidence to justify your answer.

$3\times 5=15$

Look at this statement: A number is divisible by $15$ when it is divisible by $3$ and by $5$. Do you think the statement is correct? Give evidence to justify your answer.