$\text{gcd}(d,40) = 5$, where $d$ has four digits. Determine the unknown $d$

Question

$$\text{gcd}(d,40) = 5$$

where $d$ has four digits. Determine the values $d$ can take.

Perhaps we can rewrite it as

$$\text{gcd}(d,40) = \text{gcd}(40,d \space (\text{mod 40}))$$

Regards

Answer 1

HINT:

We want $d$ such that $$\gcd(d,2^3\cdot5)=5.$$ This means that $d$ can have any prime factorisation (with four digits), but must have a factor of $5$ and cannot be even...

Answer 2

Note that $40=5\times 2^3$ so $d$ would need to be a multiple of $5$ but not a multiple of $2$ which means any number ending in $5$.