three is the number of digits you see
their sum is between sixteen and twenty three
the number is also a multiple of four
the first digit is more than five and prime.
The first digit is 7 because that's the only
digit that is more than 5 and prime.
The statement
"their sum is between sixteen and twenty three"
does not tell if it is inclusive of 16 and 23 or
exclusive of them.
If it's "inclusive", these are the solutions.
728 = 4×182, and 7+2+8 = 17
736 = 4×184, and 7+3+6 = 16
748 = 4×187, and 7+4+8 = 19
756 = 4×189, and 7+5+6 = 18
764 = 4×191, and 7+6+4 = 17
768 = 4×192, and 7+6+8 = 21
772 = 4×193, and 7+7+2 = 16
776 = 4×194, and 7+7+6 = 20
784 = 4×196, and 7+8+4 = 19
788 = 4×197, and 7+8+8 = 23
792 = 4×198, and 7+9+2 = 18
796 = 4×199, and 7+9+6 = 22
If it's "exclusive", omit the three red solutions.
Edwin