Divisibility Rule of 168

The divisibility rule for 168 is a method by which we can find out if a number is divisible by 168 or not without using the division method. Check whether 4032 is divisible by 168 with the divisibility rule.
 

Step 1: Check if the number is divisible by 8. First, look at the last three digits. If the last three digits are divisible by 8, then the entire number is divisible by 8. Here for 4032, the last three digits are 032. Since 32 is divisible by 8, we proceed.
 

Step 2: Check if the number is divisible by 3. Add up all the digits of the number, 4+0+3+2=9. Since 9 is divisible by 3, we proceed.
 

Step 3: Check if the number is divisible by 7. Use the divisibility rule of 7: double the last digit and subtract it from the rest of the number. If the result is divisible by 7, then the number is divisible by 7. For 4032, double the last digit (2×2=4) and subtract it from 403, getting 403-4=399. Since 399 is not divisible by 7, 4032 is not divisible by 168.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 168.
 

• Know the multiples of 168: Memorize the multiples of 168 (168, 336, 504, etc.) to quickly check divisibility. If your checks confirm the number is divisible by 8, 3, and 7, then the number is divisible by 168.
   
• Use negative numbers: If the result we get after applying the rule is negative, 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 they can easily check. For example, check if 16800 is divisible by 168. The last three digits are 800, which is divisible by 8. The sum of all digits is 1+6+8+0+0=15, which is divisible by 3. Use the rule for 7 on 1680. Double 0 to get 0 and subtract from 168 to get 168, which is divisible by 7. Therefore, 16800 is divisible by 168.
   
• 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 to verify and also learn.
   

• Divisibility rule: A set of rules used to determine if a number is divisible by another number without division.
   
• Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 168 are 168, 336, 504, etc.
   
• Integers: Numbers that include all whole numbers, negative numbers, and zero.
   
• Subtraction: A process of finding the difference between two numbers by reducing one number from another.
   
• Checking divisibility: The process of determining whether a number can be divided evenly by another number.