Divisibility Rule of 619

The divisibility rule for 619 is a method by which we can find out if a number is divisible by 619 or not without using the division method. Check whether 1238 is divisible by 619 with the divisibility rule.  

Step 1: Multiply the last digit of the number by 2, here in 1238, 8 is the last digit, multiply it by 2. 8 × 2 = 16 

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 123–16 = 107.

Step 3: As it is shown that 107 is not a multiple of 619, therefore, the number is not divisible by 619. If the result from step 2 was a multiple of 619, then the number would be divisible by 619.

Learning the divisibility rule will help students master division. Let’s learn a few tips and tricks for the divisibility rule of 619.

Know the multiples of 619:  

Memorize the multiples of 619 (619, 1238, 1857, 2476, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 619, then the number is divisible by 619.

Use the negative numbers:  

If the result we get after the subtraction 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 619.  
For example: Check if 3714 is divisible by 619 using the divisibility test.  

Multiply the last digit by 2, i.e., 4 × 2 = 8.  

Subtract the remaining digits excluding the last digit by 8, 371–8 = 363.  

Still, 363 is a large number, hence we will repeat the process again and multiply the last digit by 2, 3 × 2 = 6.  

Now subtracting 6 from the remaining numbers excluding the last digit, 36–6 = 30.  

As 30 is not a multiple of 619, 3714 is not divisible by 619.

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 to 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 even numbers.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 619 are 619, 1238, 1857, etc.

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

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

• Verification: The process of confirming whether the result of a divisibility test is correct, often done by actual division.