Q. The total number of four digit numbers such that each of the first three digits is divisible by the last digit, is equal to ______.
Solution:
Let the number is $abcd$, where $a,b,c$ are divisible by $d$.
No. of such numbers
$d = 1$
$9 \times 10 \times 10=900$
$d = 2$
$4 \times 5 \times 5=100$
$d = 3$
$3 \times 4 \times 4=48$
$d = 4$
$2 \times 3 \times 3 =18$
$d = 5$
$1 \times 2 \times 2 =4$
$d = 6, 7, 8, 9$
$4 \times 4 = 16$
$1086$
| No. of such numbers | |
|---|---|
| $d = 1$ | $9 \times 10 \times 10=900$ |
| $d = 2$ | $4 \times 5 \times 5=100$ |
| $d = 3$ | $3 \times 4 \times 4=48$ |
| $d = 4$ | $2 \times 3 \times 3 =18$ |
| $d = 5$ | $1 \times 2 \times 2 =4$ |
| $d = 6, 7, 8, 9$ | $4 \times 4 = 16$ |
| $1086$ |