Divisibility Rules

Divisibility

If a and m are two integers, than a is a divisor of m, or m is divisible by a when:

a | m \Leftrightarrow \exists n : n \in ℕ \land n \cdot a = m

(a | m) \land (a | n) \Rightarrow (a | m \cdot n) \land (a | (m + n)) \land (a | | m - n |)

(a | b) \land (b | c) \Rightarrow a | c

(p \in ℙ) \land (p | m \cdot n) \Rightarrow (p | m) \lor (p | n)

2\|n	last digit of n ∈{0,2,4,6,8}
3\|n	sum of all digts is divisible by 3
4\|n	last 2 digits are divisible by 4
5\|n	last digit of n ∈{0,5}
6\|n	n is divisible by both 2 and 3
8\|n	last three digits are divisible by 8
9\|n	sum of all digts is divisible by 9
10\|n	last digit of n is 0
25\|n	last two digits of n ∈{100,25,50,75}

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