A number that is divisible by 6 is either divisible by 2 or 3
Answer (1)
A number is divisible by 6 if and only if it is divisible by both 2 and 3. Let's break this down step-by-step:
Divisibility by 2 : A number is divisible by 2 if it is an even number. This means its last digit must be 0, 2, 4, 6, or 8.
Divisibility by 3 : A number is divisible by 3 if the sum of its digits is divisible by 3. For example, the number 123 is divisible by 3 because the sum of its digits (1 + 2 + 3 = 6) is divisible by 3.
Divisibility by 6 : For a number to be divisible by 6, it must satisfy both conditions above—it must be divisible by both 2 and 3.
To clarify, it's incorrect to say that a number divisible by 6 is either divisible by 2 or 3. It must be divisible by both.
For example, consider the number 12:
It is divisible by 2 because it is an even number.
It is also divisible by 3 because the sum of its digits (1 + 2 = 3) is divisible by 3.
Therefore, 12 is divisible by 6 because it meets both conditions. This means to determine if a number is divisible by 6, check whether it's divisible by both 2 and 3.
