Divisibility Rule of 119

The divisibility rule for 119 is a method by which we can determine if a number is divisible by 119 without using the division method. Check whether 238 is divisible by 119 with the divisibility rule.

Step 1: Check if the number is divisible by both 7 and 17, since 119 = 7 × 17.

Step 2: Use the divisibility rule for 7: Multiply the last digit of the number by 2, here in 238, 8 is the last digit, multiply it by 2. 8 × 2 = 16.

Step 3: Subtract the result from Step 2 from the remaining values, excluding the last digit. i.e., 23 - 16 = 7.

Step 4: Since 7 is a multiple of 7, 238 is divisible by 7.

Step 5: Use the divisibility rule for 17: Double the last digit and subtract it from the rest of the number. If the result is divisible by 17, then the number is divisible by 17.

Step 6: Double the last digit of 238 (8), i.e., 16. Subtract 16 from the rest of the number, 23 - 16 = 7.

Step 7: Since 7 is not divisible by 17, 238 is not divisible by 119.

Knowing the divisibility rules for 7 and 17 will help you easily apply the rule for 119. Let’s learn a few tips and tricks for the divisibility rule of 119.

• Memorize the multiples of 119: Knowing multiples like 119, 238, 357, etc., will help you quickly determine divisibility.

• Understand how to apply the rules for both 7 and 17: Since 119 is the product of 7 and 17, understanding these rules is crucial.

• Practice the process for large numbers: For large numbers, keep applying the divisibility rules for 7 and 17 until you reach a small number.

• Verify using the division method: To confirm, you can always use the division method to verify your results.

• Divisibility rule: A method used to determine if a number is divisible by another number without direct division.

• Multiple: A number that is the product of a given number and an integer. E.g., multiples of 119 are 119, 238, 357, etc.

• Integer: A whole number that can be positive, negative, or zero.

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

• Verification: The act of confirming the accuracy of a result, often using an alternative method like direct division.