There are 128 three-digit numbers divisible by 7.
This can be solved using arithmetic progression (AP). The smallest three-digit number divisible by 7 is 105 (7 x 15), and the largest is 994 (7 x 142). These numbers form an arithmetic sequence with a common difference of 7. The formula to find the number of terms in an AP is:
n = (last term - first term) / common difference + 1
Substituting the values, we get:
n = (994 - 105) / 7 + 1 = 128
Therefore, there are 128 three-digit numbers divisible by 7. Multiple sources confirm this result. For example, Byju's explains this using the same arithmetic progression method, noting that the three-digit numbers divisible by 7 are 105, 112, 119,..., 994, forming an AP. Similarly, Doubtnut and other sources independently arrive at the same answer of 128.
Understanding the Solution
- First Term (a): 105 (the smallest three-digit multiple of 7)
- Last Term (l): 994 (the largest three-digit multiple of 7)
- Common Difference (d): 7 (since we're considering multiples of 7)
- Number of Terms (n): Calculated using the formula above.
