How Many Odd Numbers Between 50 and 66 Are Divisible by 5?
When discussing numbers that are both odd and divisible by 5 within a specific range, clarity is essential. The question at hand is: how many odd numbers between 50 and 66 are divisible by 5? Let's break down the requirements and find the answer.
Understanding the Problem
The fundamental concepts involved are:
Odd Numbers: These are integers that, when divided by 2, leave a remainder of 1. In other words, they end in 1, 3, 5, 7, or 9. Divisibility by 5: A number is divisible by 5 if it ends in 0 or 5.Solving the Problem
To find the odd numbers between 50 and 66 that are divisible by 5, we focus on numbers that end in 5. This is because an integer divided by 5 cannot have a units digit other than 0 or 5, and since we are searching for odd numbers, the only possible choice is 5.
Identifying the Numbers
The numbers between 50 and 66 that end in 5 are:
55 65Both of these numbers satisfy the criteria of being odd and divisible by 5. Therefore, there are exactly two such numbers in the range from 50 to 66.
Conclusion
Thus, the answer to the question is that there are two odd numbers between 50 and 66 that are divisible by 5. These numbers are 55 and 65.
Additional Insights
It's worth noting that if the range was inclusive of the endpoints (i.e., from 50 to 66 inclusive), the answer would be slightly different. In that case, the number 50 would also be considered. Since 50 is even, it does not meet the criteria, but it's interesting to observe the scope of the problem.
Another interesting observation is the distribution of odd and even numbers within a range. Since every fifth number is divisible by 5, we can easily identify these numbers by checking the units digit. For odd numbers specifically, these would occur at positions 1, 3, 5, 7, and 9 in the number sequence.
FAQs
What if the number range was inclusive?
If the range was from 50 to 66 inclusive, the only change would be that 50 would be considered. However, since 50 is even, it doesn't change the count of odd numbers divisible by 5, as only 55 and 65 satisfy the criteria.
Can there be any other solutions?
No, there cannot be any other solutions. The only numbers that are both odd and divisible by 5 end in 5. Therefore, within the range of 50 to 66, the only numbers meeting both criteria are 55 and 65.
Are there any practical applications for this knowledge?
Understanding the distribution of numbers with specific properties can be useful in various fields, including mathematics, computer science, and data analysis. For example, in programming, you might need to filter or manipulate arrays based on specific criteria.
By mastering these concepts, you can tackle a wide range of problems in numerical analysis and problem-solving. Whether you're a student, a professional, or just curious, knowing how to identify and work with specific number sets is a valuable skill.