# Divisibility criteria

We know how to find the divisors of a given number, by dividing it by different candidate numbers.

Nevertheless, there are some simple rules that allow us, at first sight, to deduce some divisors.

A number is divisible by $$2$$ if it ends with a $$0$$ or an even number.

$$44, 56, 238, 70, 92, 122$$.

A number is divisible by $$3$$ if the sum of its digits is $$3$$ or a multiple of $$3$$.

$$363, 54, 81, 111, 1.320, 207$$.

A number is divisible by $$4$$ if its last two digits are zeros or multiples of $$4$$.

$$408, 300, 1.216, 312, 43.332, 5.000$$

A number is divisible by $$5$$ if it ends with a $$0$$ or a $$5$$.

$$45, 500, 134.325, 34.200, 665, 10$$.

A number is divisible by $$6$$ if it is divisible by $$2$$ and also by $$3$$.

$$3.030, 4.410, 36, 12, 132, 66$$.

A number is divisible by $$7$$ if the difference of the number without the digit of the units and the double of the digit of the units is $$0$$ or a multiple of $$7$$.

$$126$$ is divisible by $$7$$ because: $$12 - (6\times 2) =12 - 12=0$$

$$224$$ is divisible by $$7$$ because: $$22 - (4\times 2) =22 - 8=14$$, that is a multiple of $$7$$.

$$567$$ is divisible by $$7$$ because: $$56 - (7\times 2) = 56 - 14=42$$, that is a multiple of $$7$$.

A number is divisible by $$9$$ if the sum of its digits gives a multiple of $$9$$.

$$333, 999, 810, 945, 360, 9.963$$

A number is divisible by $$10$$ if the digit of the units is $$0$$.

$$20, 43.340, 620, 34.230, 100.000, 440$$

A number is divisible by $$11$$ if the difference of the sum of the digits that are in even places and in odd places is $$0$$ or a multiple of $$11$$.

$$242$$ is divisible by $$11$$ because: $$(2+2) - 4 = 4 - 4=0$$

$$616$$ is divisible by $$11$$ because: $$(6+6) - 1=12 - 1 =11$$

$$96.954$$ is divisible by $$11$$ because: $$(9+9+4) - (6+5) = 22 - 11=11$$

A number is divisible by $$25$$ if its last two digits are zeros or a multiple of $$25$$.

$$3.300, 1.250, 375, 25.425, 100, 25.050$$

A number is divisible by $$125$$ if its last three digits are zeros or a multiple of $$125$$.

$$20.000, 1.250, 34.125, 375, 501.125, 1.000$$