Number theory

Divisibility Rules

Keywords:

Divisibility

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

a|m n:nn·a=m

Divisibility Rules

a|m a|na|m·na|m+na||m-n|
a|b b|ca|c
pp|m·np|mp|n

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}