Divisibility Rule of 109

The divisibility rule for 109 is a method by which we can find out if a number is divisible by 109 or not without using the division method. Check whether 2180 is divisible by 109 with the divisibility rule.

Step 1: Take the last two digits of the number. Here in 2180, 80 is the last two digits. Multiply the last two digits by 9. 80 × 9 = 720.

Step 2: Subtract the result from Step 1 from the remaining part of the number. i.e., 21 - 720 = -699.

Step 3: Since -699 is not a multiple of 109, 2180 is not divisible by 109. If the result from step 2 is a multiple of 109, then the number is divisible by 109.

Learning the divisibility rule will help individuals master division. Let’s learn a few tips and tricks for the divisibility rule of 109.

Know the multiples of 109:

Memorize the multiples of 109 (109, 218, 327, 436, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 109, then the number is divisible by 109.

Handle negative numbers appropriately:

If the result after the subtraction is negative, we should consider the absolute value for checking the divisibility of a number.

Repeat the process for large numbers:

Individuals should keep repeating the divisibility process until they reach a small number that is divisible by 109. For example, check if 3279 is divisible by 109 using the divisibility test. Take the last two digits, 79, multiply by 9, i.e., 79 × 9 = 711. Subtract 711 from the remaining number excluding the last two digits, 32 - 711 = -679. Since -679 is not a multiple of 109, 3279 is not divisible by 109.

Use the division method to verify:

Individuals 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 it ends with an even digit.

• Multiples: Multiples are the results obtained after multiplying a number by an integer. For example, multiples of 109 are 109, 218, 327, etc.

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

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

• Absolute value: The non-negative value of a number without regard to its sign. For example, the absolute value of -5 is 5.