Product of a digit with a shell script

How do I get the product of a 1 number in bash? (12345 > 1x2x3x4x5)

I am trying to get a script to do multiplication, I have tried escaping the * char but no luck, I have also tried fiddling with expr.

echo -n "Enter number "
read n

len=$(echo $n | wc -c)

len=$(( $len - 1 ))

for (( i=1; i <= $len; i++ ))
do
   prod=$(($prod \* $(echo $n | cut -c $i) ))
done
echo "Product of $n is $prod"