Question:
Find the remainder, without performing actual division, when 798 is divided by 11.
Solution:
$798=$ A multiple of $11+$ (Sum of its digits at odd places $-$ Sum of its digits at even places)
$798=$ A multiple of $11+(7+8-9)$
$798=$ A multiple of $11+(15-9)$
$798=$ A multiple of $11+6$
Therefore, the remainder is 6 .
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