Let the number is abc. Then
a+b=4,a=0
100a+10b+c+100a+b+10c+
+100b+10a+c+100b+a+10c+
+100c+10a+b+100c+a+10b=1998
222(a+b+c)=1998
a+b+c=9
c=9−4=5 The possible numbers are
135,225,315,405The 8 factors of 135 are: 1,3,5,9,15,27,45,135
The 9 factors of 225 are: 1,3,5,9,15,25,45,75,225
The 12 factors of 315 are: 1,3,5,7,9,15,21,35,45,63,105,315
The 10 factors of 405 are: 1,3,5,9,15,27,45,81,1305,405
Therefore the number is 135.
Comments