There are 112 three-digit numbers that are divisible by 8.
To understand this, we can look at the range of three-digit numbers, which spans from 100 to 999. We need to find the smallest and largest numbers in this range that are multiples of 8.
According to the provided reference, the first three-digit number divisible by 8 is 104 (since 13 x 8 = 104). The largest three-digit number divisible by 8 is 992. The reference states that these numbers, divisible by 8, form an arithmetic sequence with a first term of 104 and a common difference of 8.
To calculate the number of terms in this arithmetic sequence, we can use the formula:
Number of terms = (Last term - First term) / Common difference + 1
Applying this to our problem:
- First term: 104
- Last term: 992
- Common difference: 8
Number of terms = (992 - 104) / 8 + 1 = 888 / 8 + 1 = 111 + 1 = 112.
Therefore, there are 112 three-digit numbers that are exactly divisible by 8.
