如何计算Divisibility
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Divisibility rules are shortcuts to determine whether one number is divisible by another without performing full division. They're used in mental arithmetic, number theory, and primality testing.
公式
Various rules: ÷2 (even), ÷3 (digit sum), ÷5 (ends 0 or 5), ÷9 (digit sum), etc.
- n
- the number being tested
- d
- the divisor (2, 3, 5, 7, 11, etc.)
分步指南
- 1÷2: last digit even
- 2÷3: sum of digits divisible by 3
- 3÷4: last two digits form number divisible by 4
- 4÷5: last digit is 0 or 5
- 5÷9: sum of digits divisible by 9
例题解析
输入
360
结果
Divisible by 2,3,4,5,6,8,9,10,12
输入
1001
结果
Divisible by 7 and 11 (and 13)
常见问题
What is the divisibility rule for 7?
One method: remove the last digit, double it, and subtract from the remaining number. Repeat until a known multiple.
What is the divisibility rule for 11?
Alternately subtract and add digits from right to left. If the result is divisible by 11, so is the original.
Are divisibility rules faster than actual division?
Yes, for quick mental checks. But for programming, direct modulo might be faster.
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