Question

The least number of 4 digits which is exactly divisible by 9 is
A. 1008
B. 1009
C. 1026
D. 1018

Answer 1

Hint: In this question, we have to find the least number of 4 digits. The thing about which we have to take the most care of is if the number being asked for is the least number of any number of digits or of the greatest number of that many digits. For solving such questions, we first write down the least number of n digits (let the number of digits being asked in the question be n). Then we apply the required divisibility rule for the number (say m) which has to divide the number of n digits. We check from the smallest number and we keep going up until we reach the number which meets the divisibility rule. And once we come across such a number, we stop, and we are going to have our answer.

Complete step-by-step answer:
We are going to use the formula of divisibility rule of 9, which is:
A number is divisible by 9, if and only if the sum of the digits of the number is divisible by 9.
Complete step by step answer:
The smallest number of 4 digits is 1000.
Now, we are going to check for each number from 1000 if it is divisible by 9.
And to do that we just need the sum of the digits of the number and if the sum is divisible by 9, then the number is divisible by 9.
\[ \Rightarrow \]Sum of digits of 1000 = 1 (not divisible)
\[ \Rightarrow \]Sum of digits of 1001 = 2 (not divisible)
\[ \Rightarrow \]Sum of digits of 1002 = 3 (not divisible)
\[ \Rightarrow \]Sum of digits of 1003 = 4 (not divisible)
\[ \Rightarrow \]Sum of digits of 1004 = 5 (not divisible)
\[ \Rightarrow \]Sum of digits of 1005 = 6 (not divisible)
\[ \Rightarrow \]Sum of digits of 1006 = 7 (not divisible)
\[ \Rightarrow \]Sum of digits of 1007 = 8 (not divisible)
\[ \Rightarrow \]Sum of digits of 1008 = 9 (divisible)
Hence, the smallest 4-digit number divisible by 9 is 1008.

Hence, the correct option is A).

Note: So, we saw that in solving questions like these, we first write down what we have to find out. Then, we write down the divisibility rule of the number which has to divide that least number. Then we start at the first number and keep going up till we have our number. And once we get the number which meets the criteria, we stop, and we are going to have our answer. But, if there is no divisibility rule defined for the number, then we write the smallest number of the n digits. Then we divide that number by m. Then, we are going to subtract the remainder from the smallest number and add m to it and we are going to have our answer.