There are 128 three-digit numbers divisible by seven.
Understanding the Solution
This problem can be solved using the concept of arithmetic progressions (AP). The three-digit numbers divisible by 7 form an arithmetic sequence.
- The smallest three-digit number divisible by 7 is 105 (7 x 15).
- The largest three-digit number divisible by 7 is 994 (7 x 142).
These numbers form an arithmetic progression with:
- First term (a) = 105
- Common difference (d) = 7
- Last term (l) = 994
The formula to find the number of terms (n) in an arithmetic progression is:
l = a + (n-1)d
Substituting the values:
994 = 105 + (n-1)7
Solving for 'n':
889 = (n-1)7
n-1 = 127
n = 128
Therefore, there are 128 three-digit numbers divisible by 7. Multiple sources (Byju's, Cuemath, Quora, Doubtnut, GMAT Club, etc.) confirm this solution.
