Are All Even Numbers Divisible By?
All even numbers are divisible by 2.
An even number is defined as any integer that can be exactly divided by 2, leaving no remainder. This means that when you divide an even number by 2, the result is a whole number. Examples include 2, 4, 6, 8, 10, -2, -4, and so on. The definition itself highlights the divisibility by 2. [Source: SplashLearn, Cuemath, Byju's]
Several sources confirm this fundamental property:
- SplashLearn: Explicitly states that "Every even number is divisible by 2."
- Cuemath: Defines an even number as "any number that is completely divisible by 2."
- Byju's: Provides examples (2, 4, 12, 10000, 10002) to demonstrate the divisibility of even numbers by 2.
Are All Even Numbers Divisible by Other Numbers?
While all even numbers are divisible by 2, it's crucial to understand that not all even numbers are divisible by other numbers. For instance:
- Not all even numbers are divisible by 4: The even number 6 is not divisible by 4. [Source: Math Answers]
- Not all even numbers are divisible by 3: The even number 4 is not divisible by 3. [Source: Quora]
However, some even numbers are divisible by 3 (e.g., 6, 12, 18) and are, of course, also divisible by 2. [Source: Quora]
The Proof
A mathematical proof for this is straightforward:
- Definition: An even number x can be expressed as 2n, where n is an integer.
- Divisibility: Since x is already expressed as 2 multiplied by an integer (n), it is, by definition, divisible by 2. [Source: Reddit r/learnmath]
