There are 100 three-digit numbers divisible by 9.
Understanding the Solution
This problem involves finding the number of multiples of 9 within the range of three-digit numbers (100 to 999). The smallest three-digit number divisible by 9 is 108 (9 x 12), and the largest is 999 (9 x 111).
To determine the total count:
- Find the first multiple: The smallest three-digit multiple of 9 is 108.
- Find the last multiple: The largest three-digit multiple of 9 is 999.
- Calculate the difference: Subtract the first multiple from the last multiple: 999 - 108 = 891.
- Divide by the divisor: Divide the difference by 9: 891 / 9 = 99.
- Add 1: Add 1 to include the first multiple: 99 + 1 = 100.
Therefore, there are 100 three-digit numbers divisible by 9. Multiple sources (Byjus.com, Quora, Doubtnut and others) confirm this answer.
Practical Insight
This type of problem demonstrates a fundamental concept in number theory – finding the number of multiples of a given number within a specific range. This approach can be generalized to find the number of multiples of any integer within any given range.
