Divisibility Rule of 61

The divisibility rule for 61 is a method by which we can determine if a number is divisible by 61 without using the division method. Check whether 2442 is divisible by 61 with the divisibility rule.

Step 1: Multiply the last digit of the number by 2, here in 2442, 2 is the last digit. Multiply it by 2. 2 × 2 = 4.

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 244–4 = 240.

Step 3: As 240 is not a multiple of 61, 2442 is not divisible by 61. If the result from Step 2 were a multiple of 61, then the number would be divisible by 61.

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 61.

Know the multiples of 61:  

Memorize the multiples of 61 (61, 122, 183, 244, 305, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 61, then the number is divisible by 61.

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 clearly divisible by 61.  
For example: Check if 3721 is divisible by 61 using the divisibility test. Multiply the last digit by 2, i.e., 1 × 2 = 2.  
Subtract the remaining digits excluding the last digit by 2, 372–2 = 370.  
Still, 370 is a large number, hence we will repeat the process again and multiply the last digit by 2, 0 × 2 = 0.  
Now subtracting 0 from the remaining numbers excluding the last digit, 37–0 = 37.  
37 is not a multiple of 61, so 3721 is not divisible by 61.

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 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 digit.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 61 are 61, 122, 183, 244, etc.

• Integers: Integers are 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: The process of confirming the correctness of a result, often by using a different method such as actual division.