Divisibility and Number Properties

Core concept

For divisibility by 11: find the difference between the sum of digits in odd positions and the sum of digits in even positions (counting from the right); if this difference is 0 or a multiple of 11, the original number is divisible by 11. For example, checking 2728: odd-position digits (8,7) sum to 15, even-position digits (2,2) sum to 4, difference is 11, so 2728 is divisible by 11 — a rule that, while more complex than others, saves considerable time compared to long division for larger numbers.