Which of the numbers given below is exactly divisible by 12?
- A14744
- B28856
- C43976
- D57228
Solution & Step-by-step Explanation
A number is exactly divisible by if it satisfies the divisibility rules for both and (, where and are co-prime numbers).
1. Divisibility Rule for 4: The last two digits of the number must be a multiple of .
* Option A: is divisible by .
* Option B: is divisible by .
* Option C: is divisible by .
* Option D: is divisible by .
All options satisfy this criterion.
2. Divisibility Rule for 3: The sum of all individual digits must be divisible by .
* Option A: (not divisible by )
* Option B: (not divisible by )
* Option C: (not divisible by )
* Option D: (since is a multiple of , this number is divisible by )
Therefore, is completely divisible by both and , making it exactly divisible by .
1. Divisibility Rule for 4: The last two digits of the number must be a multiple of .
* Option A: is divisible by .
* Option B: is divisible by .
* Option C: is divisible by .
* Option D: is divisible by .
All options satisfy this criterion.
2. Divisibility Rule for 3: The sum of all individual digits must be divisible by .
* Option A: (not divisible by )
* Option B: (not divisible by )
* Option C: (not divisible by )
* Option D: (since is a multiple of , this number is divisible by )
Therefore, is completely divisible by both and , making it exactly divisible by .