Divisibility Rule of 177

The divisibility rule for 177 is a method to check if a number is divisible by 177 without using division. Let's see whether 3549 is divisible by 177 using this rule.
 

Step 1: Multiply the last digit of the number by 20, here in 3549, 9 is the last digit, so multiply it by 20. 9 × 20 = 180.
 

Step 2: Subtract the result from Step 1 from the remaining number but do not include the last digit. i.e., 354–180 = 174.
 

Step 3: Since 174 is not a multiple of 177, the number 3549 is not divisible by 177. If the result from step 2 were a multiple of 177, then the number would be divisible by 177.
 

Learning the divisibility rule can help kids master division. Let's learn a few tips and tricks for the divisibility rule of 177.
 

• Know the multiples of 177: Memorize the multiples of 177 (177, 354, 531, 708, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 177, then the number is divisible by 177.
   
• Use the negative numbers: If the result we obtain after subtraction is negative, disregard the sign and consider it as positive for checking divisibility.
   
• Repeat the process for large numbers: Students should repeat the divisibility process until they reach a small number that is divisible by 177.
  
  For example: Check if 6213 is divisible by 177 using the divisibility test. Multiply the last digit by 20, i.e., 3 × 20 = 60. Subtract the remaining digits excluding the last digit by 60, 621–60 = 561.  
  
  Since 561 is still a large number, repeat the process. Multiply the last digit by 20, 1 × 20 = 20. Now subtracting 20 from the remaining numbers excluding the last digit, 56–20 = 36.
  
  Since 36 is not a multiple of 177, 6213 is not divisible by 177.
   
• Use the division method to verify: Students can use the division method to verify and cross-check their results. This will help them verify and also learn.
   

• Divisibility rule: The set of rules used to determine 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 obtained after multiplying a number by an integer. For example, multiples of 177 are 177, 354, 531, 708, etc.
   
• Integers: Integers are the numbers that include all whole numbers, negative numbers, and zero.
   
• Subtraction: Subtraction is the process of finding the difference between two numbers by reducing one number from another.
   
• Verification: This involves using another method, such as division, to confirm the results obtained from the divisibility rule.