Question

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

Answer 1

Answer: 1086

Let the number is $abcd$, where $a,b,c$ are divisible by $d$.

	No. of such numbers
$d=1$	$9\times 10\times 10=900$
$d=2$	$4\times 5\times 5=100$
$d=3$	$3\times 4\times 4=48$
$d=4$	$2\times 3\times 3=18$
$d=5$	$1\times 2\times 2=4$
$d=6,7,8,9$	$4\times 4=16$
	$1086$