All natural numbers divisible by 2 are even numbers, and they can be represented as: 2, 4, 6, 8, 10, 12, 14, 16, and so on, continuing infinitely.
Understanding Natural Numbers and Divisibility
- Natural Numbers: These are positive integers starting from 1 (1, 2, 3, 4, ...).
- Divisibility: A number is divisible by 2 if the result of the division is a whole number (an integer) without any remainder.
Identifying Numbers Divisible by 2
A simple test for divisibility by 2 is to check if the last digit of the number is 0, 2, 4, 6, or 8. If it is, the entire number is divisible by 2. Since natural numbers begin at 1, the first natural number divisible by 2 is 2. The next is 4 (2 x 2), then 6 (2 x 3), and so on. The pattern continues indefinitely, creating an infinite sequence of even natural numbers.
Examples of Natural Numbers Divisible by 2
- 2 (2 / 2 = 1)
- 4 (4 / 2 = 2)
- 6 (6 / 2 = 3)
- 8 (8 / 2 = 4)
- 10 (10 / 2 = 5)
- 12 (12 / 2 = 6)
- 100 (100 / 2 = 50)
- 1000 (1000 / 2 = 500)
- 1002 (1002 / 2 = 501)
Representation as a Set
The set of all natural numbers divisible by 2 can be represented as:
{2, 4, 6, 8, 10, 12, 14, 16, ...}
This is an infinite set, as there is no upper limit to the natural numbers.
In conclusion, the natural numbers divisible by 2 are all the even positive integers, forming an infinite set starting with 2.
