Find if a Number is Divisible by 19

A brief tutorial which explains the divisibility rule for 19. Using this rule you could identify whether the given number is divisible by 19 without performing the long division. It has two cases to find divisibility. Refer the below two rules and find if the given number is divisible by 19.

Divisibility Rule for 19

Rule 1:

Multiply the last digit by 2. Add the resultant value to the remaining numbers. Apply this rule over and over again as necessary.

Example

Find if the number 101156 is divisible by 19.

Solution :

Applying the divisibility rule for 19,

Step 1:

Multiplying the lat digit by 2, we get

2 x 6 = 12

Step 2:

Add the resultant value to the remaining numbers

10115 + 12 = 10127

Step 3:

Repeat the same steps as step 1 & step 2 until the number becomes smaller to get easily divisible by 19

1012 + 2 x 7 = 1026

Step 4:

102 + 2 x 6 = 114

Step 5:

Now, it is known that 114 is divisible by 19 (i.e) 114 = 6 x 19

Hence, the number 101156 is also divisible by 19.

Rule 2:

Multiply the last two digits by 4. Add the resultant value to the remaining numbers. Apply this rule over and over again as necessary.

Example 2:

Find if the number 11343 is divisible by 19.

Solution :
Step 1:

Multiplying the last two digits by 4, we get
(i.e) 43 x 4 = 172

Step 2:

Add the resultant value to the remaining numbers
172 + 113 = 285

Step 3:

Repeat the same steps as step 1 & step 2 until the number becomes smaller to get easily divisible by 19

85 x 4 + 2 = 342

Step 4:

42 x 4 + 3 = 171

Step 5:

Now, it is clear that 171 is divisible by 19 (i.e) 19 x 9 = 171

Since, the number 171 is divisible by 19, the original number 11343 is also divisible by 19.


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