Divisibility Rule of 561

The divisibility rule for 561 is a method to check if a number is divisible by 561 without dividing. Let's examine whether 1683 is divisible by 561 using this rule.  

Step 1: Multiply the last digit of the number by a factor, specific to 561. (For example, if the factor is 3, multiply the last digit by 3.)

Here, in 1683, the last digit is 3. Multiply it by 3: 3 × 3 = 9.  

Step 2: Subtract the result from Step 1 from the remaining number, excluding the last digit. For example, 168 - 9 = 159.  
 

Step 3: Check if the result (159 in this case) is divisible by 561. If it is, then the original number is divisible by 561. If it's not, then the original number isn't divisible by 561.

Knowing the divisibility rule helps simplify division. Here are some tips and tricks for understanding the divisibility rule of 561:

• Memorize multiples of 561: Knowing the multiples of 561 can quickly confirm divisibility.

• Handle negative results: If the subtraction leads to a negative number, treat it as positive to check divisibility.

• Repeat the process for large numbers: Keep applying the divisibility process on large numbers until you reach a smaller number that is clearly divisible by 561.  

• Verify with division: Use traditional division to cross-check and confirm results, enhancing understanding.

• Divisibility rule: A set of procedures to determine if one number is divisible by another without direct division.

• Multiples: Numbers obtained by multiplying a given number by an integer.

• Factor: A number that divides another number exactly without leaving a remainder.

• Integer: A whole number that can be positive, negative, or zero.

• Subtraction: The process of taking one number away from another to find the difference.