How Many Numbers Between 100 and 999 are Divisible by 7?

There are 128 numbers between 100 and 999 that are divisible by 7.

This can be calculated using the following method:

1. Find the smallest three-digit number divisible by 7: The smallest three-digit number is 100. Dividing 100 by 7 gives a quotient of 14 with a remainder of 2. Therefore, the smallest three-digit number divisible by 7 is 105 (7 x 15).

2. Find the largest three-digit number divisible by 7: The largest three-digit number is 999. Dividing 999 by 7 gives a quotient of 142 with a remainder of 5. Therefore, the largest three-digit number divisible by 7 is 994 (7 x 142).

3. Calculate the number of multiples: The number of multiples of 7 between 105 and 994 (inclusive) can be found by subtracting the smallest from the largest, dividing by 7, and adding 1 (to include both endpoints): (994 - 105) / 7 + 1 = 128

Multiple sources confirm this result:

• Study.com states: "So there are total 128 numbers in between 100 to 999 which are divisible by 7."
• Quora shows the calculation: (994–105)/7 +1=128
• Vaia confirms: "Thus, there are 128 integers between 100 and 999 that are divisible by 7."