D3
Divisibility Filtering
整除筛选
Parity / 奇偶与整除Grades G5 - G8
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What It Looks Like
Recognition signals — when you see these, think of this structure:
- 1Divisible by a specific number
- 2Multiple of something
- 3Factor conditions on the answer
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What It Really Tests
The core mathematical idea behind this structure:
Use divisibility conditions as filters to narrow candidates instead of testing blindly.
用整除条件作为过滤器来缩小候选范围, 而不是逐个检验。
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Why Students Get Stuck
Common mistakes to watch out for:
- ⚠Checking numbers one by one without strategy
- ⚠Using only one factor condition when there are several
- ⚠Ignoring combined constraints (e.g. divisible by 6 = divisible by 2 AND 3)
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Your First Step
How to begin thinking about problems with this structure:
Break the divisibility condition into factor requirements first.
先把整除条件分解成因子要求。
Related Structures
These structures share similar patterns or thinking approaches: