Divisibility Rule of 769

The divisibility rule for 769 is a method by which we can find out if a number is divisible by 769 or not without using the division method. Let's check whether 1538 is divisible by 769 with the divisibility rule.
 

Step 1: Multiply the last digit of the number by 2. In 1538, 8 is the last digit, so multiply it by 2. 8 × 2 = 16.
 

Step 2: Subtract the result from Step 1 from the remaining digits, excluding the last digit. i.e., 153–16 = 137.
 

Step 3: As it is shown that 137 is not a multiple of 769, the number 1538 is not divisible by 769. If the result from step 2 is a multiple of 769, then the number is divisible by 769.
 

Learning the divisibility rule will help students master division. Let’s learn a few tips and tricks for the divisibility rule of 769.
 

• Know the multiples of 769: 
  Memorize the multiples of 769 (769, 1538, 2307, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 769, then the number is divisible by 769.
   
• Use negative numbers:
  If the result we get after 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 769.
  
  For example, check if 3076 is divisible by 769 using the divisibility test. Multiply the last digit by 2, i.e., 6 × 2 = 12.
  
  Subtract the remaining digits excluding the last digit by 12, 307–12 = 295. Still, 295 is a large number, hence we will repeat the process again.
  
  Multiply the last digit by 2, 5 × 2 = 10. Now subtract 10 from the remaining numbers excluding the last digit, 29–10 = 19. Since 19 is not a multiple of 769, 3076 is not divisible by 769.
   
• 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 performing division.
   
• Multiples: Numbers obtained by multiplying a given number by an integer. For example, multiples of 769 are 769, 1538, 2307, etc.
   
• Integers: Numbers that include all whole numbers, negative numbers, and zero.
   
• Subtraction: A process of finding the difference between two numbers by reducing one number from another.
   
• Verification: The process of confirming the correctness of a result, often by using an alternative method such as direct division.