There are 11 numbers between 1 and 100 (inclusive) that are divisible by 9.
Understanding Divisibility by 9
A number is divisible by 9 if the sum of its digits is divisible by 9. For example:
- 81: 8 + 1 = 9, which is divisible by 9. Therefore, 81 is divisible by 9.
- 36: 3 + 6 = 9, which is divisible by 9. Therefore, 36 is divisible by 9.
- 99: 9 + 9 = 18, which is divisible by 9. Therefore, 99 is divisible by 9.
Calculating the Numbers
To find how many numbers between 1 and 100 are divisible by 9, we can perform simple division:
100 รท 9 = 11 with a remainder of 1.
This indicates that there are 11 multiples of 9 between 1 and 100. These are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and 99.
Multiple sources confirm this:
- Reference 1: Explicitly states there are 11 numbers divisible by 9 between 1 and 100.
- Reference 2: Reinforces that there are 11 numbers divisible by 9 between 1 and 100.
- Reference 3: While focusing on numbers divisible by 4 or 9, it confirms the 11 divisible by 9.
- Reference 4: In the context of a larger problem, the solution relies on 11 numbers being divisible by 9.
- Reference 5: While including other constraints, it notes there are 11 numbers divisible by 9 from 1 to 100.
- Reference 6: Explicitly lists all 11 numbers between 1 and 100 divisible by 9.
- Reference 7: This source tackles a similar problem with different bounds, but confirms the logic applied to arrive at 11.
- Reference 8: This source, dealing with numbers divisible by 4, implicitly supports the method and answer for numbers divisible by 9.
- Reference 9: Similar to Reference 7, confirming the process for finding multiples.
- Reference 10: Discusses divisibility rules, supporting the method's validity.
