Number theory

# Divisibility Rules

## Divisibility

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

## Divisibility Rules

$\left(a|m\right)\wedge \left(a|n\right)⇒\left(a|m·n\right)\wedge \left(a|\left(m+n\right)\right)\wedge \left(a||m-n|\right)$
$\left(p\in \mathrm{ℙ}\right)\wedge \left(p|m·n\right)⇒\left(p|m\right)\vee \left(p|n\right)$

## Divisibility rules for numbers

 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}