**Divisibility Tests**

**How can you know that a particular large number is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10 or 11.**

This article will help you to learn about divisibility tests for numbers 2 to 11.

**Divisibility Test for 2:**

If, the last digit of a given number is divisible by 2 then the given number itself is also divisible by 2.

**Example:** We want to test if 278956 is divisible by 2. We can see that its last digit which is 6, is divisible by 2. It means the number itself 278956 is also divisible by 2. You can consider taking different examples and verify this test.

**Divisibility Test for 3:**

Suppose, we are given a large number and we want to check if that particular given number is divisible by 3. We sum up all the digits of number. If, sum of all the digits is divisible by 3 then the number itself is also divisible by 3.

**Example: **We want to check if 12789 is divisible by 3 or not. We sum up all the digits of 12789 (1 + 2 + 7 + 8 + 9 = 27). The sum of digits which is equal to 27, is divisible by 3. It means the given number itself which is 12789, is also divisible by 3. You can verify this test by considering different examples.

**Divisibility Test for 4:**

Suppose, we are given a large number and we want to check if that particular given number is divisible by 4. We check the last two digits of number. If, the last two digits of number are divisible by 4 then it means the number itself is also divisible by 4.

**Example:** We want to check if 128920 is divisible by 4 or not. We just check the last two digits of 128920, the last two digits make 20 which is divisible by 4. It means the number itself which is 128920, is also divisible by 4. You can verify this test by considering different examples.

**Divisibility Test for 5:**

Suppose, we are given a large number and we want to check if that particular given number is divisible by 5. If, the last digit is either 0 or 5 then the given number is divisible by 5.

**Example: **We want to check if 154780 is divisible by 5 or not. We just check the last digit of number. It is 0 which means the given number 154780, is divisible by 5.

**Divisibility Test for 6:**

Suppose, we are given a large number and we want to check if that particular given number is divisible by 6. A given number is divisible by 6 only if the number is divisible by both 2 and 3. Therefore, we apply divisibility tests of both 2 and 3 on a given number.

**Example: **We want to check if 154872 is divisible by 6 or not. We apply divisibility tests of 2 and 3 on this number.

According to divisibility test of 2, the last digit is divisible by 2 which means the number 154872 is also divisible by 2.

According to divisibility test of 3, the sum of digits (1 + 5 + 4 + 8 + 7 + 2 = 27) is divisible by 3, which means the number 154872 is also divisible by 3.

Because, the number is divisible by both 2 and 3. It means the number is also divisible by 6.

**Divisibility Test for 7:**

Suppose, we are given a large number and we want to check if that particular given number is divisible by 7. We just multiply the last digit of number by 2 and then subtract the result from the rest of the number. We keep on repeating the process till we get a number which we can directly say that it is divisible or not divisible by 7. It will be more clear through an example.

**Example: **We want to check if 2401 is divisible by 7 or not. We multiply its last digit by 2.

The last digit is 1. Multiplying it by 2. We get (1 x 2 = 2). We subtract result from the rest of the number which is 240.

We get 240 - 2 = 238

We repeat the process again. We multiply the last digit by 2 and then subtract the result from the rest of the number.

Multiplying last digit by 2, we get (8 x 2 = 16). Subtracting result from the rest of the number, we get (23 - 16 = 7).

Now, we are sure that 7 is divisible by 7. It means that the number from where we started (2401) is also divisible by 7.

Lets suppose at the end we get a number 13. Then, we would be sure that it is not divisible by 7. It would mean that the number from where we started would also not be divisible by 7.

**Divisibility Test for 8:**

Suppose, we are given a large number and we want to check if that particular number is divisible by 8. We check the last three digits of number. If, the last three digits of number are divisible by 8 then it means the number itself is also divisible by 8.

**Example:** We want to check if 128160 is divisible by 8 or not. We just check the last three digits of 128160, the last three digits make 160 which is divisible by 8. It means the given number itself which is 128160, is also divisible by 8. You can verify this test by considering different examples.

**Divisibility Test for 9:**

Suppose, we are given a large number and we want to check if that particular given number is divisible by 9. We sum up all the digits of a given number. If, sum of all the digits is divisible by 9 then the given number itself is also divisible by 9.

**Example: **We want to check if 12789 is divisible by 9 or not. We sum up all the digits of 12789 (1 + 2 + 7 + 8 + 9 = 27). The sum of digits which is equal to 27, is divisible by 9. It means the number itself which is 12789 is also be divisible by 9. You can verify this test by considering different examples.

**Divisibility Test for 10:**

The given number is divisible by 10 if the last digit of a given number is 0. For example, we are given a number 48750 and we want to check if it is divisible by 10 or not. We just check the last digit of number. It is zero which means 48750 is divisible by 10. If, it is not zero then the given number would not be divisible by 10.

**Divisibility Test for 11:**

Just understand divisibility test of 11 by example. Suppose, we want to check if the number 14641 is divisible by 11 or not.

**Step 1**: We start from the left most digit and sum up the digits skipping one digit at a time while moving to the right direction.

The left most digit is 1. We take 1 into consideration. We skip one digit now which is 4. The next digit is 6. We take 6 into consideration. We skip the next one which is 4. We consider the next one which is 1.

We sum up all the digits which were considered: (1 + 6 + 1 = 8). The sum is equal to 8.

**Step 2: **We sum up all the digits which were skipped in step 1. The sum is (4 + 4 = 8).

**Step 3: **We subtract the sum calculated in step 2 from the sum calculated in step 1. We get (8 - 8 = 0).

Now, we know that 0 is divisible by 11 which means the number 14641 from where we started, is also divisible by 11. {0 is divisible by any number}

For example, in step 3, we get result equal to 22. We know that 22 is divisible by 11. It would mean that the number from we started would also be divisible by 11.

For example, in step 3. we get result equal to 7. We know that 7 is not divisible by 11. It would mean that the number from we started would not be divisible by 11.