Divisibility Rule of 277

The divisibility rule for 277 is a method by which we can determine if a number is divisible by 277 without using the division method. Check whether 83081 is divisible by 277 using the divisibility rule.

Step 1: Multiply the last digit of the number by 2. Here in 83081, 1 is the last digit. Multiply it by 2. 1 × 2 = 2.  

Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last digit. i.e., 8308 - 2 = 8306.  

Step 3: Repeat the above steps with the result until you determine its divisibility by 277. If a resulting number is a multiple of 277, then the original number is divisible by 277. 

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 277.

Know the multiples of 277:  

Memorize the multiples of 277 (277, 554, 831, 1108, etc.) to quickly check for divisibility. If the result from the subtraction is a multiple of 277, then the number is divisible by 277.

Use the negative numbers:  

If the result we get after subtraction is negative, we will ignore 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 277.  
For example: Check if 49769 is divisible by 277 using the divisibility test.   
Multiply the last digit by 2: 9 × 2 = 18.  
Subtract the result from the remaining digits (excluding the last digit): 4976 - 18 = 4958.  
Repeat: 4958 is still large, so multiply the last digit by 2: 8 × 2 = 16.  
Now, subtract 16 from the remaining numbers: 495 - 16 = 479.  
Since 479 is not a multiple of 277, 49769 is not divisible by 277.

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 277 are 277, 554, 831, 1108, etc.

• Integers: Integers are the numbers that include all 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: Verification is the process of confirming that the result obtained is correct by using another method, such as division, to check the answer.