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

Question

Aicharya · Accepted Answer

Let the last be d , so total following cases will be there for first three numbers, No. of such numbers d = 1 , 9 &#215; 10 &#215; 10 = 900 d = 2 4 &#215; 5 &#215; 5 = 100 d = 3 3 &#215; 4 &#215; 4 = 48 d = 4 2 &#215; 3 &#215; 3 = 18 d = 5 1 &#215; 2 &#215; 2 = 4 Similarly for d = 6 , &#160; 7 , &#160; 8 , &#160; 9 4 &#215; 4 = 16 1086

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

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

Solution