Odd numbers are numbers that leave a remainder of 1 when divided by 2. They are not divisible by 2. However, odd numbers can be divisible by other numbers.
Divisibility of Odd Numbers
Odd numbers are divisible by:
- Odd numbers: Any odd number is divisible by itself and 1. For example, 9 is divisible by 9 and 1. Also, 9 is divisible by 3 (another odd number).
- Other integers: Some odd numbers are divisible by other integers besides 1 and themselves. For example:
- 9 is divisible by 3.
- 15 is divisible by 3 and 5.
- 21 is divisible by 3 and 7.
- 25 is divisible by 5.
- Not by 2: Crucially, odd numbers are never divisible by 2. This is the defining characteristic of an odd number. The provided text states: "Odd numbers are numbers which when divided by 2 leave the remainder 1."
Examples of Odd Number Divisibility
Let's look at some examples to illustrate:
- 5: Divisible by 1 and 5.
- 9: Divisible by 1, 3, and 9.
- 15: Divisible by 1, 3, 5, and 15.
- 21: Divisible by 1, 3, 7, and 21.
It is important to note that while odd numbers are not divisible by 2, many are divisible by other odd numbers. The divisibility of an odd number depends on its specific prime factorization.
