# Divisibility Rules: 2, 4, 8 and 5, 10

Let's look at three of the divisibility rules:

The Rule for

**2**: Any whole number that ends in 0, 2, 4, 6, or 8 will be divisible by 2.

Example:

Example:

**456,791,824**

This is the number four hundred fifty-six thousand, seven hundred ninety-one, eight hundred twenty-four. We can tell if 2 divides into this number without a remainder by just looking at the last digit.

456,791,824 - the last digit is a 4. This means that the number is EVEN and 2 will divide into it without a remainder. 456,791,824 is divisible by 2.

**Example:**

**34,807**

Check out the last digit of this number. 34,807 - the last digit is a 7. This means that the number is ODD and 2 will not divide into it evenly. There will be a remainder. So 34,807 is not divisible by 2.

The Rule for

**4**: If the last two digits of a whole number are divisible by 4, then the entire number is divisible by 4.

**Example:**

**456,791,824**

For this rule, we will look at the last two digits: 456,791,824. Does 4 divide evenly into 24? Yes. That means that 4 will also divide evenly into 456,791,824 and there will be no remainder.

**Example:**

**723,810**

Again, we will take a look at the last two digits: 723,810. Does 4 divide evenly into 10? No. That means that 4 will not divide evenly into 7223,810 and there will be a remainder.

The Rule for

**8**: If the last three digits of a whole number are divisible by 8, then the entire number is divisible by 8.

**Example:**

**456,791,824**

For this rule, we will look at the last three digits of the number: 456,791,824. Does 8 divide evenly into 824? YES, 8 goes into 824, 103 times without anything left over. So this number is divisible by 8.

**Example:**

**923,780**

Again, we will focus on the last three digits of the number: 923,780. Does 8 divide evenly into 780? NO, 8 goes into 780, 97 times with a remainder of 4. So this number is not divisible by 8

The rules for 2, 4, and 8 should all look similar. That is because these numbers are related. Think about the powers of 2.

**2**

**=**

^{1}**2**

**2**

**=**

^{2}**4**

**2**

**=**

^{3}**8**

The exponent, or power of two, used is also the number of digits that we have to use when performing the test.

The Rule for

**5**: Number that are divisible by 5 must end in 5 or 0.

**Example:**

**34,780**

For this rule we just look at the last digit: 34,780. The last digit is a 0, so this number is divisible by 5.

**Example:**

**13,569**

Again, we will focus our attention on the last digit: 13,569. The last digit is a 9, so this number is not divisible by 5.

The Rule for

**10**: Numbers that are divisible by 10 need to be even and divisible by 5, because the prime factors of 10 are 5 and 2. Basically, this means that for a number to be divisible by 10, the last digit must be a 0.

**Example:**

**23,890**

Take a look at the last digit: 23,890. The last digit is a 0. So this number is even and divisible by 5. That means that it is also divisible by 10.

**Example:**

**85,395**

Take a look at the last digit: 85,395. The last digit is a 5. So this number is odd and divisible by 5. Because the number is not even, it is not divisible by 10. It has to end in 0 to be divisible by 10.

**Let's put it all together. Take a look at this example.**

**1,782,645,988**

This number ends in 8....

It is divisible by 2, but it is not divisible by 5 or 10.

This number ends in 88....

It is divisible by 4 because 4 goes into 88 evenly.

This number ends in 988....

It is not divisible by 8 because 8 does not go into 988 evenly.

**45,981,400**

This number ends in 0....

It is divisible by 2, 5, and 10.

This number ends in 00....

It is divisible by 4. (You might be thinking, "Hey, 4 doesn't divide evenly into 00", but it shows that 4 needs to go into a multiple of 100. 4 goes into 100 evenly, so it will go into multiples of 100 evenly as well.)

This number ends in 400....

It is divisible by 8 because 8 will go into 400, 50 times with no remainder.

**How are the divisibility rules helpful?**

The divisibility rules help us to find factors of numbers. Instead of actually having to do the long division, we can use the rule to determine if the number is a factor first before dividing and getting an answer.

**Related Links:**

Math

Fractions

Factors