Divisibility Rules for 2, 4, and 10

In this article, we will teach you the best and simplest tricks to identify if a number is divisible by $2$, by $4$, and by $10$.

Shall we start?

A number is divisible by $2$ if its units digit is even.
Let's remember that an even digit is one that can be divided by $2$ without leaving a remainder.
If the units digit is odd, we can determine, without a doubt, that the number is not divisible by $2$.

Divisibility by 2 - example 1
The number $48$
Let's observe the units digit $8$
$8$ is even, therefore, we can determine that the number $48$ is divisible by $2$.

Divisibility by 2 - example 2
The number $677$
Let's observe the units digit $7$.
$7$ is odd, therefore, we can determine that $677$ is not divisible by $2$.

Divisibility by 2 - example 3
Determine if the number $3578$ is divisible by $2$.

Solution:
The units digit is $8$, even, therefore, the number is divisible by $2$.

Divisibility by 2 - example 4

Determine if the number $10003$ is divisible by $2$

Solution:
The units digit is $3$, odd, therefore, the number is not divisible by $2$.

To find out if a certain number is divisible by $4$ we will teach you $2$ ways to do it:

A number is divisible by 4 if its last two digits are divisible by 4.

Divisibility by 4, (First method) - example 1

The number $832$
The last two digits are $32$. $32$ is divisible by $4$, therefore, we will determine that $832$ is divisible by $4$.

Divisibility by 4, (First method) - example 2
The number $56712$
The last two digits are $12$. $12$ is divisible by $4$, therefore, we can determine that $56712$ is as well.

Divisibility by 4, (First method) - example 3
The number $415$
The last two digits are $15$. $15$ is not divisible by $4$, therefore, we will determine that $415$ is not either.

Multiply the tens digit by 2 and add the units digit. If the result is a multiple of 4, the original number is also.

Divisibility by, (Second method) - example 1
The number $832$
Let's multiply the tens digit $3$ by $2$ and add the units digit $2$:
$3\times 2+2=8$
$8$ is divisible by $4$, therefore, we will determine that $832$ is as well.

Divisibility by, (Second method) - example 2
The number $56712$
Let's multiply the tens digit $1$ by $2$ and add the units digit $2$:
$1\times 2+2=4$
$4$ is divisible by $4$, therefore, we will determine that $56712$ is also $4$.

Divisibility by, (Second method) - example 3
The number $415$
Let's multiply the tens digit $1$ by $2$ and add the units digit $5$:
$1\times 2+5=7$
$7$ is not divisible by $4$ therefore, we will determine that $415$ is not either.

A number is divisible by $10$ if its units digit is $0$.
Divisibility by 10 - example 1
Is the number $480$ divisible by $10$?
The units digit is $0$ therefore, we can determine that $480$ is divisible by $10$.

Divisibility by 10 - example 2
Is the number $567$ divisible by $10$?
The units digit is $7$ and not $0$. Consequently, the number $567$ is not divisible by $10$.

Divisibility by 10 - example 3
Is the number $65860$ divisible by $10$?
The units digit is $0$, therefore, we can determine that the number $65860$ is divisible by $10$.

In third grade $A$ there are $4$ students, in third grade $B$ there are $2$ students, and in third grade $C$ there are $10$ students.
If we have $120$ balloons, in which grade could the balloons be distributed equally, without any remainder?

Answer: in all grades.

Solution:
Let's see if the number $120$ is divisible by $4$.
Take the last pair of digits $20$. $20$ is divisible by $4$, therefore, $120$ is divisible by $4$.
Let's see if the number $120$ is divisible by $2$.
The units digit is $0$ even, therefore, $120$ is divisible by $2$.
Let's see if the number $120$ is divisible by $10$.
The units digit is $0$, therefore, the number is divisible by $10$.