How many three-digit numbers are divisible by 7?

The smallest three-digit number is 100 and the largest is 999.

To find the number of three-digit numbers divisible by 7, we need to find the number of multiples of 7 between 100 and 999, inclusive.

First, find the smallest three-digit multiple of 7.
Divide 100 by 7: 100 ÷ 7 ≈ 14.28
The next whole number is 15, so the smallest three-digit multiple of 7 is 7 * 15 = 105.

Next, find the largest three-digit multiple of 7.
Divide 999 by 7: 999 ÷ 7 ≈ 142.71
The largest whole number is 142, so the largest three-digit multiple of 7 is 7 * 142 = 994.

Now we need to find the number of multiples of 7 between 105 and 994, inclusive. This is an arithmetic sequence with first term a₁ = 105, last term aₙ = 994, and common difference d = 7.

The formula for the nth term of an arithmetic sequence is: aₙ = a₁ + (n-1)d

We can use this to find n (the number of terms):
994 = 105 + (n-1)7
889 = (n-1)7
889/7 = n-1
127 = n-1
n = 128

Therefore, there are 128 three-digit numbers divisible by 7.