Divisibility Rule of 449

The divisibility rule for 449 is a method by which we can find out if a number is divisible by 449 or not without using the division method.

Check whether 1347 is divisible by 449 with the divisibility rule.  

Step 1: Multiply the last digit of the number by 9. For 1347, 7 is the last digit, so multiply it by 9. 7 × 9 = 63.

Step 2: Subtract the result from Step 1 from the remaining part of the number but do not include the last digit. i.e., 134–63 = 71.

Step 3: As it is shown that 71 is not a multiple of 449, the number is not divisible by 449. If the result from step 2 were a multiple of 449, then the number would be divisible by 449.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 449. 

• Know the multiples of 449:  Memorize the multiples of 449 (449, 898, 1347, 1796…etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 449, then the number is divisible by 449.
   
• Use the negative numbers:  If the result we get after the subtraction is negative, ignore the negative sign 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 449.  
  
  For example: Check if 4041 is divisible by 449 using the divisibility test. 
  
  Multiply the last digit by 9, i.e., 1 × 9 = 9.  Subtract the remaining digits excluding the last digit by 9, 404–9 = 395. 
  
  Since 395 is still large, repeat the process: multiply the last digit by 9, 5 × 9 = 45. 
  
  Now subtract 45 from the remaining numbers excluding the last digit, 39–45 = -6. 
  
  Since 6 is not a multiple of 449, 4041 is not divisible by 449.
   
• 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 verify and also learn.

• Divisibility Rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 2 if the number ends with an even digit.
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 449 are 449, 898, 1347, 1796, etc.
   
• Integers: Integers are the numbers that include all whole numbers, negative numbers, and zero.
   
• Subtraction: Subtraction is the process of finding out the difference between two numbers by reducing one number from another.
   
• Verification: The process of confirming the accuracy of a result, such as using division to check if a number is divisible by another number.