awk filter numbers inbetween

Hi,

I have a file which has a number in each line ( i think they are strings )
I will have a $first and $last variable, which are strings but contains only numbers. Also a file $f, I want to filter out the lines in $f with only numbers in between $first and $last. Do I need to consider the string format and have to change it to numbers first?

Thanks.

Assuming space as delimiter

awk -v Frst=$first -v Last=$last ' $1 >= Frst && $1 <= Last ' $f

thank you!