Divisibility Rule For 27 With Examples

Divisibility Rule For 27

The divisibility rule for 27 involves checking if a number is divisible by (27) based on the properties of its digits. Here’s a detailed explanation of the rule and examples to illustrate how to apply it.

Divisibility Rule for 27

The divisibility rule for 27 states that a number is divisible by 27 if, after applying a specific operation involving its digits, the result is divisible by 27. The rule involves multiplying the last digit of the number by 8, subtracting this result from the rest of the number and checking if the final result is divisible by 27 then the number is divisible by 27.

Steps of the Rule:

1. Identify the Number: Take a number to check for divisibility by 27.
2. Separate the Digits: Identify the last digit and the rest of the number.
3. Multiply the Last Digit by 8: Take the last digit and multiply it by 8.
4. Subtract from the Rest: Subtract the result from the number formed by the remaining digits.
5. Check the Result: Determine if the result is divisible by 27. If it is, then the original number is also divisible by 27.

Example 1: Check if 369 is divisible by 27

1. Identify the Number: 369
2. Separate the Digits: Last digit = 9, Rest of the number = 36
3. Multiply the Last Digit by 8: (9 x 8 = 72)
4. Subtract from the Rest: (36 – 72 = -36)
5. Check the Result: -36 is not divisible by 27 (since (-36 / 27 = -1.33)), which is not divisible. So, 369 is not divisible by 27.

Example 2: Check if 810 is divisible by 27

1. Identify the Number: 810
2. Separate the Digits: Last digit = 0, Rest of the number = 81
3. Multiply the Last Digit by 8: (0 x 8 = 0)
4. Subtract from the Rest: (81 – 0 = 81)
5. Check the Result: 81 is divisible by 27 (since (81 / 27 = 3)). Therefore, 810 is divisible by 27.

Example 3: Check if 540 is divisible by 27

1. Identify the Number: 540
2. Separate the Digits: Last digit = 0, Rest of the number = 54
3. Multiply the Last Digit by 8: (0 x 8 = 0)
4. Subtract from the Rest: (54 – 0 = 54)
5. Check the Result: 54 is divisible by 27 (since (54 / 27 = 2)). So, 540 is divisible by 27.

Summary of the Rule

• The rule can help quickly assess whether large numbers are divisible by 27 without performing full division.

By practicing with various numbers, we can become adept at applying this rule to determine divisibility by 27 efficiently.