Divisibility Rule of 167

The divisibility rule for 167 is a method by which we can find out if a number is divisible by 167 or not without using the division method. Check whether 2501 is divisible by 167 with the divisibility rule.  

Step 1: Multiply the last digit of the number by 5, here in 2501, 1 is the last digit; multiply it by 5. 1 × 5 = 5  

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 250–5 = 245.
 
Step 3: As it is shown that 245 is not a multiple of 167, therefore, the number is not divisible by 167. If the result from step 2 is a multiple of 167, then the number is divisible by 167.
 

Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 167. 
 

• Know the multiples of 167: Memorize the multiples of 167 (167, 334, 501, 668, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 167, then the number is divisible by 167. 
   
• 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 167.
  
  For example: Check if 5012 is divisible by 167 using the divisibility test. Multiply the last digit by 5, i.e., 2 × 5 = 10.
  
  Subtract the remaining digits excluding the last digit by 10, 501–10 = 491. Still, 491 is a large number, hence we will repeat the process again and multiply the last digit by 5, 1 × 5 = 5.
  
  Now subtracting 5 from the remaining numbers excluding the last digit, 49–5 = 44. As 44 is not a multiple of 167, 5012 is not divisible by 167.
   
• 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 even numbers.
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 167 are 167, 334, 501, etc.
   
• Integers: Integers are the numbers that include all the 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 correctness of a result or calculation, often by performing an additional method such as division to check divisibility.