Divisibility Rule of 83

The divisibility rule for 83 is a technique to determine if a number is divisible by 83 without using the division method. Let's check whether 415 is divisible by 83 using the divisibility rule.

Step 1: Multiply the last digit of the number by 5. In 415, 5 is the last digit, so multiply it by 5. 5 × 5 = 25.

Step 2: Subtract the result from Step 1 from the remaining values, excluding the last digit. i.e., 41 - 25 = 16.

Step 3: Since 16 is not a multiple of 83, 415 is not divisible by 83. If the result from step 2 is a multiple of 83, then the number is divisible by 83.

Learning the divisibility rule will help students master division. Let’s explore a few tips and tricks for the divisibility rule of 83.

Know the multiples of 83:

Memorize the multiples of 83 (83, 166, 249, 332, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 83, then the number is divisible by 83. If the result we get after 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 repeat the divisibility process until they reach a small number that is divisible by 83.

For example, check if 7476 is divisible by 83 using the divisibility test. Multiply the last digit by 5, i.e., 6 × 5 = 30.

Subtract 30 from the remaining digits, excluding the last digit: 747 - 30 = 717.

Repeat the process: 7 × 5 = 35. Subtract 35 from the remaining numbers: 71 - 35 = 36.

Since 36 is not a multiple of 83, 7476 is not divisible by 83.

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: A set of rules used to determine whether a number is divisible by another number without performing division.

• Multiples: The results obtained after multiplying a number by an integer. For example, multiples of 83 are 83, 166, 249, 332, etc.

• Integers: Numbers that include all whole numbers, negative numbers, and zero.

• Subtraction: The process of finding the difference between two numbers by reducing one number from another.

• Verification: The process of confirming the accuracy of a calculation or result, often by using an alternative method.