Divisibility Rule of 683

The divisibility rule for 683 is a method to find out if a number is divisible by 683 without using the division method. Check whether 2049 is divisible by 683 using this rule.
 

Step 1: Multiply the last digit of the number by 5; in 2049, 9 is the last digit, so multiply it by 5. 9 × 5 = 45
 

Step 2: Subtract the result from Step 1 from the remaining values, excluding the last digit. That is, 204 – 45 = 159.
 

Step 3: As it is evident that 159 is not a multiple of 683, the number is not divisible by 683. If the result from Step 2 were a multiple of 683, then the number would be divisible by 683.
 

Learning the divisibility rule can help students master division. Let’s explore a few tips and tricks for the divisibility rule of 683.
 

• Know the multiples of 683: Memorize the multiples of 683 (683, 1366, 2049, etc.) to quickly check divisibility. If the result from subtraction is a multiple of 683, then the number is divisible by 683.
   
• Use negative numbers: If the result obtained after subtraction is negative, ignore the negative sign and consider it as positive for checking divisibility.
   
• Repeat the process for large numbers: Students should continue repeating the divisibility process until they reach a small number that is divisible by 683.
  
  For example, check if 4098 is divisible by 683 using the divisibility test. Multiply the last digit by 5, i.e., 8 × 5 = 40.
  
  Subtract the remaining digits excluding the last digit by 40, 409 – 40 = 369.
  
  Since 369 is not a multiple of 683, 4098 is not divisible by 683.
   
• Use the division method to verify: Students can verify their results by using the division method. This helps them confirm their findings and learn the process better.
   

• Divisibility rule: A set of steps used to determine if one number is divisible by another without performing division.
   
• Multiples: The results obtained by multiplying a number by an integer. For example, multiples of 683 are 683, 1366, 2049, etc.
   
• Integers: Numbers that include all whole numbers, their negatives, and zero.
   
• Subtraction: A process of finding the difference between two numbers by taking one number away from another.
   
• Verification: The process of confirming the correctness of a result, often involving additional methods such as division.