Divisibility Rule For 18 With Examples

To determine if a number is divisible by 18, it must satisfy the divisibility rules for both 2 and 9, since (18 = 2 x 9).

1. Divisibility Rule for 2:

A number is divisible by 2 if its last digit is even. This means the last digit can be 0, 2, 4, 6, or 8.

2. Divisibility Rule for 9:

A number is divisible by 9 if the sum of its digits is divisible by 9.

Combining the Rules for 18:

For a number to be divisible by 18, it must:

• Have an even last digit (to be divisible by 2)
• Have the sum of its digits divisible by 9 (to be divisible by 9)

Examples:

1. Example: 162

• Last digit: 2 (even, so divisible by 2)
• Sum of digits: (1 + 6 + 2 = 9) (which is divisible by 9)
• Since both conditions are met, 162 is divisible by 18.

1. Example: 234

• Last digit: 4 (even, so divisible by 2)
• Sum of digits: (2 + 3 + 4 = 9) (which is divisible by 9)
• Both conditions are met, so 234 is divisible by 18.

1. Example: 180

• Last digit: 0 (even, so divisible by 2)
• Sum of digits: (1 + 8 + 0 = 9) (which is divisible by 9)
• Both conditions are satisfied, so 180 is divisible by 18.

1. Example: 85

• Last digit: 5 (not even, so not divisible by 2)
• No need to check the sum, as it already fails the first condition.
• 85 is not divisible by 18.

1. Example: 306

• Last digit: 6 (even, so divisible by 2)
• Sum of digits: (3 + 0 + 6 = 9) (which is divisible by 9)
• Both conditions are met, thus 306 is divisible by 18.

Conclusion:

To check if a number is divisible by 18, verify that it meets both the conditions of being even (for 2) and having a digit sum that is a multiple of 9. This method can quickly help determine divisibility without direct division.