Divisibility Rule of 89

The divisibility rule for 89 is a method by which we can determine if a number is divisible by 89 without using the division method. Check whether 2673 is divisible by 89 with the divisibility rule.
 

Step 1: Multiply the last digit of the number by 9. Here in 2673, 3 is the last digit, so multiply it by 9. 3 × 9 = 27.
 

Step 2: Subtract the result from Step 1 from the remaining values, excluding the last digit. i.e., 267–27 = 240.
 

Step 3: Repeat the process for the result from Step 2. Multiply the last digit (0) by 9. 0 × 9 = 0. Subtract from the remaining number: 24–0 = 24.
 

Step 4: Since 24 is not a multiple of 89, 2673 is not divisible by 89. If the result from the repeated process is a multiple of 89, then the number is divisible by 89.
 

Learning the divisibility rule helps kids master division. Let’s learn a few tips and tricks for the divisibility rule of 89.
 

• Know the multiples of 89: Memorize the multiples of 89 (89, 178, 267, 356, 445, etc.) to quickly check divisibility. If the result from subtraction is a multiple of 89, then the number is divisible by 89.
   
• 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 89.
  
  For example, check if 7125 is divisible by 89 using the divisibility test. Multiply the last digit by 9, i.e., 5 × 9 = 45. Subtract from the remaining digits excluding the last digit: 712–45 = 667.
  
  Repeat the process: multiply the last digit (7) by 9, 7 × 9 = 63. Subtract from the remaining number: 66–63 = 3. Since 3 is not a multiple of 89, 7125 is not divisible by 89.
   
• 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: A set of rules used to find out whether a number is divisible by another number. For example, a number is divisible by 2 if the number ends with an even digit.
   
• Multiples: Multiples are the results obtained after multiplying a number by an integer. For example, multiples of 89 are 89, 178, 267, 356, etc.
   
• Integers: Integers are numbers that include all whole numbers, negative numbers, and zero.
   
• Subtraction: Subtraction is the process of finding the difference between two numbers by reducing one number from another.
   
• Verification: The process of confirming the correctness of a calculation or result, often by using an alternative method like division.