Divisibility Rule of 67

The divisibility rule for 67 is a method by which we can find out if a number is divisible by 67 or not, without using the division method. Check whether 4021 is divisible by 67 with the divisibility rule.  

Step 1: Multiply the last digit of the number by 5, here in 4021, 1 is the last digit, multiply it by 5. 1 × 5 = 5.  

Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last digit. i.e., 402–5 = 397.

Step 3: As it is shown that 397 is not a multiple of 67, therefore, the number is not divisible by 67. If the result from step 2 is a multiple of 67, then the number is divisible by 67.

Learn the divisibility rule to help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 67.

Know the multiples of 67:  

Memorize the multiples of 67 (67, 134, 201, 268, 335… etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 67, then the number is divisible by 67.

Use 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 67.  
For example: Check if 13421 is divisible by 67 using the divisibility test.  
Multiply the last digit by 5, i.e., 1 × 5 = 5.  
Subtract the remaining digits excluding the last digit by 5, 1342–5 = 1337.  
Still, 1337 is a large number, hence we will repeat the process again and multiply the last digit by 5, 7 × 5 = 35.  
Now subtracting 35 from the remaining numbers excluding the last digit, 133–35 = 98.  
Since 98 is not a multiple of 67, 13421 is not divisible by 67.

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 67 are 67, 134, 201, 268, 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 using another method, such as division, to confirm or cross-check the correctness of a solution.