Question

Which of the following numbers are divisible by 4?
A. 23
B. 1216
C. 1200
D. 235

Answer 1

Hint:Here, instead of dividing all the four numbers by 4, which is a very lengthy process, we can use a divisibility test for 4. Divisibility tests and rules help us to find if a number is divisible by a certain factor without performing actual division.
For example: Divisibility rule for 2: The number should be an even number; that is, the unit digit of the number should be 0,2,4,6 or 8.
Divisibility rule for 3: The sum of the digits of the number should be divisible by 3.
Divisibility rule for 4: The number formed by the last two digits of the number should be divisible by 4.

Complete step by step answer:
As we know that divisibility rules help us know if a certain number is a factor of the given number or not. We know that the divisibility rule of 4 is: The number formed by the last two digits of the number should be divisible by 4.

Let’s proceed by examining every option.
A. 23
The number formed by the last two digits is the number itself which is 23. We know that 23 is not divisible by 4. It leaves a remainder of 3. Hence, 23 is not divisible by 4.

B. 1216
The number formed by the last two digits is 16. We all know that 16 is perfectly divisible by 4 and hence, 1216 is also divisible by 4.

C. 1200
The number formed by the last two digits is 00. We know that 0 is divisible by 4, and hence the number 1200 is also divisible by 4.

D. 235
The number formed by the last two digits is 35. We know that 35 is not divisible by 4. When divided by 4, it leaves a remainder of 3. Therefore, 235 is also not divisible by 4.

After checking divisibility rule for all the four options, the answer is: B and C.

Note:Having a good idea about the divisibility rules will help us solve this problem easily. We can also check our answers by performing actual division. Divisibility rules exist for various numbers 2,3,4,5,6 and so on. They reduce the complication of the problem and save a lot of time because for numbers like 7,11,13 the division becomes tougher.