Divisibility Rule of 219

The divisibility rule for 219 is a method by which we can find out if a number is divisible by 219 or not without using the division method. Check whether 438 is divisible by 219 with the divisibility rule.  

Step 1: Multiply the last digit of the number by 20, here in 438, 8 is the last digit, multiply it by 20. 8 × 20 = 160

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit, i.e., 43–160 = -117.

Step 3: As it is shown that -117 is not a multiple of 219, therefore, the number is not divisible by 219. If the result from step 2 is a multiple of 219, then the number is divisible by 219.

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 219. 

Know the multiples of 219:

Memorize the multiples of 219 (219, 438, 657, 876, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 219, then the number is divisible by 219.

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 219. 

For example: Check if 657 is divisible by 219 using the divisibility test. Multiply the last digit by 20, i.e., 7 × 20 = 140. Subtract the remaining digits excluding the last digit by 140, 65–140 = -75. Still, -75 is not a multiple of 219, hence 657 is not divisible by 219.

Use the division method to verify:

Students can use the division method as a way to verify and cross-check 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 219 if the process described results in a multiple of 219.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 219 are 219, 438, 657, 876, 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.

• Verify: To confirm the accuracy of a mathematical process or result, often by using an alternative method such as division.