The total number of four digit numbers such that each of first three digits is divisible by the last

Question

The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to

Professor PC Thomas Classes · Answer

(1086) : If the unit digit is 1\\ total number $=4 	imes 5 	imes 5=100$\ If the unit digit is 3 , then $3 	imes 4 	imes 4$\ $=48$ numbers If the unit digit is 4 , then $2 	imes 3 	imes 3$\ $=18$ numbers\ If the unit digit is 5 , then $1 	imes 2 	imes 2$\ $=4$ numbers\ If the unit digit is 6 , then $1 	imes 2 	imes 2$\ $=4$ numbers\ Similarly, if the unit digit is 7,8 or 9 then $4+4+4=12$ numbers\ Total possible numbers\ $=900+100+48+18+20=1086$\