Divisibility Rule of 91

The divisibility rule for 91 is a method by which we can find out if a number is divisible by 91 or not without using the division method. Check whether 728 is divisible by 91 with the divisibility rule.  

Step 1: Check if the number is divisible by both 7 and 13, as 91 is the product of these two prime numbers (7 × 13). 

Step 2: Use the divisibility rule for 7 first. Multiply the last digit by 2, here in 728, 8 is the last digit, multiply it by 2. 8 × 2 = 16.

Step 3: Subtract the result from Step 2 from the remaining values but do not include the last digit. i.e., 72–16 = 56.

Step 4: 56 is a multiple of 7, so 728 is divisible by 7.

Step 5: Now, check divisibility by 13. Double the last digit and add it to the rest of the number. 8 × 2 = 16, and 72 + 16 = 88.

Step 6: 88 is a multiple of 13, so 728 is also divisible by 13.

Since 728 is divisible by both 7 and 13, it is divisible by 91.
 

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 91.

• Know the multiples of 91: Memorize the multiples of 91 (91, 182, 273, 364, etc.) to quickly check divisibility. If the result of the checks is divisible by both 7 and 13, then the number is divisible by 91.
   
• Use the breakdown method: If a number is large, break it down into smaller parts and check each part's divisibility by 7 and 13.
   
• Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by both 7 and 13.
  
  For example: Check if 1820 is divisible by 91 using the divisibility test. First, check divisibility by 7: Multiply the last digit by 2, i.e., 0 × 2 = 0. Subtract 0 from the remaining digits, 182–0 = 182. 
  
  Check 182: Multiply the last digit by 2, 2 × 2 = 4. Subtract from the remaining digits, 18–4 = 14.14 is a multiple of 7, so 1820 is divisible by 7.
  
  Now, check divisibility by 13: Double the last digit and add it to the rest of the number, 0 × 2 = 0, and 182 + 0 = 182. 182 is a multiple of 13, so 1820 is divisible by 13. Since 1820 is divisible by both 7 and 13, it is divisible by 91.
   
• 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.
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 91 are 91, 182, 273, 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.
   
• Prime numbers: Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. For example, 7 and 13 are prime factors of 91.