Yes, all even numbers are divisible by 2. This is the very definition of an even number.
Understanding Even Numbers
An even number is defined as any integer that is perfectly divisible by 2, meaning the division leaves no remainder. This is supported by numerous sources:
- SplashLearn: "Every even number is divisible by 2. That is, any number that ends with 2, 4..." https://www.splashlearn.com/math-vocabulary/division/divisible
- Cuemath: "An even number is any number that is completely divisible by 2." https://www.cuemath.com/numbers/even-numbers/
- Byjus: The statement "All even numbers are divisible by 2" is explicitly stated as true. https://byjus.com/question-answer/all-even-numbers-are-divisible-by-2-state-whether-the-statement-is-true-or-false/
- SparkNotes: "All even numbers are divisible by 2." https://www.sparknotes.com/math/prealgebra/wholenumbers/section2/
Examples
Here are some examples illustrating this:
- 2 ÷ 2 = 1
- 4 ÷ 2 = 2
- 6 ÷ 2 = 3
- 100 ÷ 2 = 50
- -8 ÷ 2 = -4 (Even numbers also include negative integers)
The divisibility by 2 is inherent in the very concept of an even number. It's not a property that needs to be proven; it's the foundational characteristic.
