Divisibility Rule of 689

The divisibility rule for 689 is a method by which we can find out if a number is divisible by 689 without using the division method. Check whether 1378 is divisible by 689 with the divisibility rule.
 

Step 1: Multiply the last digit of the number by 2. In 1378, 8 is the last digit, so 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., 137–16 = 121.
 

Step 3: Since 121 is not a multiple of 689, the number is not divisible by 689. If the result from Step 2 were a multiple of 689, then the number would be divisible by 689.
 

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 689.
 

• Know the multiples of 689: Memorize the multiples of 689 (689, 1378, 2067, ...) to quickly check divisibility. If the result from the subtraction is a multiple of 689, then the number is divisible by 689.
   
• Use the negative numbers: If the result we get after the subtraction is negative, consider its absolute value for checking divisibility.
   
• Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 689.
  
  For example, check if 2756 is divisible by 689 using the divisibility test. Multiply the last digit by 2, i.e., 6 × 2 = 12.
  
  Subtract 12 from the remaining digits excluding the last digit, 275–12 = 263. Since 263 is still a large number, repeat the process. Multiply the last digit by 2, 3 × 2 = 6.
  
  Subtracting 6 from the remaining numbers excluding the last digit, 26–6 = 20. Since 20 is not a multiple of 689, 2756 is not divisible by 689.
   
• 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: A set of rules used to determine whether a number is divisible by another number without direct division. 
   
• Multiples: The results we get after multiplying a number by an integer. For example, multiples of 689 are 689, 1378, 2067, ...
   
• Integers: Numbers that include all whole numbers, negative numbers, and zero.
   
• Subtraction: The process of finding the difference between two numbers by reducing one number from another.
   
• Absolute value: The non-negative value of a number without regard to its sign. For example, the absolute value of -20 is 20.