Divisibility Rule of 19

The divisibility rule for 19 is a method by which we can find out if a number is divisible by 19 or not without using the division method.

Check whether 266 is divisible by 19 with the divisibility rule.  

Step 1: Multiply the last digit of the number by 2, here in 266, 6 is the last digit, multiply it by 2. 6 × 2 = 12 

Step 2: Add the result from Step 1 to the remaining values but do not include the last digit. i.e., 26 + 12 = 38.

Step 3: As it is shown that 38 is not a multiple of 19, the number is not divisible by 19. If the result from step 2 is a multiple of 19, then the number is divisible by 19.

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 19.

• Know the multiples of 19: Memorize the multiples of 19 (19, 38, 57, 76, 95…etc.) to quickly check the divisibility. If the result from the addition is a multiple of 19, then the number is divisible by 19.

• Use the negative numbers: If the result we get after the addition is negative, we will avoid the symbol and consider it as positive for checking the divisibility of a number.

• Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 19.
  
   For example: Check if 1147 is divisible by 19 using the divisibility test.  Multiply the last digit by 2, i.e., 7 × 2 = 14.  Add the remaining digits excluding the last digit by 14, 114 + 14 = 128.  
  
  Still, 128 is a large number, hence we will repeat the process again and multiply the last digit by 2, 8 × 2 = 16.  Now adding 16 to the remaining numbers excluding the last digit, 12 + 16 = 28.  As 28 is not a multiple of 19, 1147 is not divisible by 19.

• Use the division method to verify: Students can use the division method as a way to verify and crosscheck their results. This will help them verify and also learn.

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 2 if the number ends with an even number.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 19 are 19, 38, 57, 76, etc.

• Integers: Integers are the numbers that include all the whole numbers, negative numbers, and zero.

• Addition: Addition is the process of combining two or more numbers to get their total or sum.

• Subtraction: Subtraction is a process of finding out the difference between two numbers by reducing one number from another.