The Highest Common Factor (HCF) of two consecutive odd numbers is 1.
Understanding HCF and Consecutive Odd Numbers
What is HCF?
The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more integers without a remainder.
What are Consecutive Odd Numbers?
Consecutive odd numbers are odd numbers that follow each other in sequence, with a difference of 2 between each number. Examples include:
- 3 and 5
- 7 and 9
- 11 and 13
Why the HCF is 1
The key reason why the HCF of two consecutive odd numbers is always 1 is that they share no common factors other than 1.
- Example: Consider the numbers 3 and 5. The factors of 3 are 1 and 3. The factors of 5 are 1 and 5. The only common factor they share is 1. As stated in the provided reference, the consecutive odd numbers cannot have a common factor other than 1.
Examples of HCF of Consecutive Odd Numbers
Here are a few more examples to illustrate this point:
| Odd Number 1 | Odd Number 2 | Factors of Odd Number 1 | Factors of Odd Number 2 | HCF |
|---|---|---|---|---|
| 7 | 9 | 1, 7 | 1, 3, 9 | 1 |
| 15 | 17 | 1, 3, 5, 15 | 1, 17 | 1 |
| 21 | 23 | 1, 3, 7, 21 | 1, 23 | 1 |
As you can see, regardless of which consecutive odd numbers you choose, their HCF will always be 1.
