Question
Which of the following numbers is divisible by both 6 and 8?
Answer: Option D
:
D
If a number is divisible by both 2 and 3, then it will bedivisible by 6 also.
Divisibility by 2
Here all the numbers, 9638, 9640, 9642, 9648 are divisible by 2 as they end with one of these (0, 2, 4, 6, 8) numbers or simply as they are even numbers.
Divisibility by 3
⇒9 + 6 + 3 + 8 = 26
⇒9 +6 + 4 + 0 = 19
⇒9 + 6 + 4 + 2 = 21
⇒9 + 6 + 4 + 8 = 27
Here only 21 and 27 are divisible by 3 hence only9642 and 9648 are divisible by 3.
So, thesetwo numbers are divisible by both 2 and 3 and hence divisible by 6.
Divisibility by 8
A number will bedivisible by 8 only if the last three digits are divisible by 8.
Thelast 3 digits of only9648, i.e. 648 is divisible by 8.
But last three digits of 9642, i.e. 642 is not divisible by 8.
9648 is divisible by both 6 and 8.
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:
D
If a number is divisible by both 2 and 3, then it will bedivisible by 6 also.
Divisibility by 2
Here all the numbers, 9638, 9640, 9642, 9648 are divisible by 2 as they end with one of these (0, 2, 4, 6, 8) numbers or simply as they are even numbers.
Divisibility by 3
⇒9 + 6 + 3 + 8 = 26
⇒9 +6 + 4 + 0 = 19
⇒9 + 6 + 4 + 2 = 21
⇒9 + 6 + 4 + 8 = 27
Here only 21 and 27 are divisible by 3 hence only9642 and 9648 are divisible by 3.
So, thesetwo numbers are divisible by both 2 and 3 and hence divisible by 6.
Divisibility by 8
A number will bedivisible by 8 only if the last three digits are divisible by 8.
Thelast 3 digits of only9648, i.e. 648 is divisible by 8.
But last three digits of 9642, i.e. 642 is not divisible by 8.
9648 is divisible by both 6 and 8.
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