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