Divisibility Rule of 867

The divisibility rule for 867 is a method by which we can determine if a number is divisible by 867 without using the division method.

Check whether 1734 is divisible by 867 using the divisibility rule.

Step 1: Multiply the last digit of the number by 2, here in 1734, 4 is the last digit, so multiply it by 2. 4 × 2 = 8.

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 173–8 = 165.

Step 3: As it is shown that 165 is not a multiple of 867, therefore, the number is not divisible by 867. If the result from step 2 were a multiple of 867, then the number would be divisible by 867.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 867.

Know the multiples of 867:

Memorize the multiples of 867 (867, 1734, 2601, 3468, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 867, then the number is divisible by 867.

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 867. For example, check if 5202 is divisible by 867 using the divisibility test. Multiply the last digit by 2, i.e., 2 × 2 = 4. Subtract the remaining digits excluding the last digit by 4, 520–4 = 516. Still, 516 is not a multiple of 867, hence 5202 is not divisible by 867.

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 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 867 are 867, 1734, 2601, etc.
   
• Integers: Integers are numbers that include all the whole numbers, negative numbers, and zero.
   
• Subtraction: Subtraction is a process of finding the difference between two numbers by reducing one number from another.
   
• Verification: Verification is the process of confirming the accuracy of a result, often using a different method like division to cross-check the divisibility.