A 3-digit number ranges from 100 to 999. We need to find how many of these numbers are divisible by 11. A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is a multiple of 11.

Fri, 01 May 2026 14:45:06 +0000

# How Many 3-Digit Numbers Between 100 and 999 Are Divisible by 11? When exploring three-digit numbers—those ranging from 100 to 999—a common question arises: How many of these numbers are divisible by 11? Understanding this not only helps in number theory but also enhances practical skills in divisibility rules. A key insight lies in the divisibility rule of 11, which states that a number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is a multiple of 11. In a 3-digit number, abc (where a, b, c are individual digits), position 1 (leftmost) is odd, position 2 is even, and position 3 is odd. Thus, the rule becomes: (a + c) − b must be divisible by 11.