Divisibility Rule of 557

The divisibility rule for 557 is a method by which we can find out if a number is divisible by 557 or not without using the division method. Check whether 1114 is divisible by 557 with the divisibility rule.
 

Step 1: Multiply the last three digits of the number by 2, here in 1114, 114 are the last three digits, multiply it by 2. 114 × 2 = 228.
 

Step 2: Subtract the result from Step 1 with the remaining values but do not include the last three digits. i.e., 1–228 = -227.
 

Step 3: As it is shown that -227 is not a multiple of 557, therefore, the number is not divisible by 557. If the result from step 2 is a multiple of 557, then the number is divisible by 557.
 

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 557.
 

• Know the multiples of 557: Memorize the multiples of 557 (557, 1114, 1671, 2228, 2785…etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 557, then the number is divisible by 557.
   
• Use the negative numbers: If the result we get after the 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 557.
  
  For example: Check if 2785 is divisible by 557 using the divisibility test. Multiply the last three digits by 2, i.e., 785 × 2 = 1570.
  
  Subtract the remaining digits excluding the last three digits by 1570, 2–1570 = -1568. Still, -1568 is a large number, hence we will repeat the process again and multiply the last three digits by 2, 568 × 2 = 1136.
  
  Now subtracting 1136 from the remaining numbers excluding the last three digits, 1–1136 = -1135. Since -1135 is not a multiple of 557, 2785 is not divisible by 557.
   
• 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. For example, a number is divisible by 2 if the number ends with an even number.
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 557 are 557, 1114, 1671, 2228, 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.
   
• Verification: The process of checking the accuracy of a calculation by using a different method, such as division, to confirm the result.