There are infinitely many numbers divisible by 6. To determine how many numbers are divisible by 6 within a specific range, you need to define that range.
Understanding Divisibility by 6
A number is divisible by 6 if and only if it's divisible by both 2 and 3. This means:
- Divisibility by 2: The number must be even (its last digit is 0, 2, 4, 6, or 8).
- Divisibility by 3: The sum of its digits must be divisible by 3.
Let's illustrate with examples:
- 12: Even (divisible by 2) and 1 + 2 = 3 (divisible by 3). Therefore, 12 is divisible by 6.
- 18: Even (divisible by 2) and 1 + 8 = 9 (divisible by 3). Therefore, 18 is divisible by 6.
- 21: Not even (not divisible by 2), therefore not divisible by 6.
- 24: Even (divisible by 2) and 2 + 4 = 6 (divisible by 3). Therefore, 24 is divisible by 6.
- 25: Not even (not divisible by 2), therefore not divisible by 6.
Finding the Number of Multiples within a Range
To find how many numbers divisible by 6 exist within a given range (e.g., between 1 and 100, between 1000 and 2000), you can use the following approach:
- Identify the first multiple: Find the smallest number in the range divisible by 6.
- Identify the last multiple: Find the largest number in the range divisible by 6.
- Calculate the count: Divide the difference between the last and first multiples by 6 and add 1. This accounts for all the multiples within the range.
Example: How many numbers between 1 and 100 are divisible by 6?
- First multiple: 6
- Last multiple: 96
- Count: (96 - 6) / 6 + 1 = 16
There are 16 numbers divisible by 6 between 1 and 100. This aligns with the example provided by Math Answers. They showed that for the range 1-50, there are 8 numbers.
The Quora links (https://www.quora.com/How-many-numbers-are-divisible-by-6, https://www.quora.com/How-many-numbers-are-divisible-by-6-between-1-to-100) also demonstrate this approach, highlighting the importance of defining the range. Numbergenerator.org provides a list of multiples, illustrating the infinite nature of the sequence.
