The question "What numbers can be divided by 18?" can be interpreted in two distinct ways, each yielding a different set of numbers:
- Numbers that divide 18 evenly (Factors of 18): These are the integers by which 18 can be divided without leaving a remainder.
- Numbers that are themselves divisible by 18 (Multiples of 18): These are the integers that, when divided by 18, result in a whole number with no remainder.
Let's explore both interpretations to provide a comprehensive answer.
Factors are numbers that, when multiplied together, produce a given number. In this context, we are looking for the numbers that can be divided into 18 with no remainder.
According to the information on "Factors of 18 by Division Method" from BYJU'S, if 18 is divided by any numbers other than 1, 2, 3, 6, 9, and 18, a remainder will be left. Therefore, the exact numbers that are the factors of 18 are:
- 1
- 2
- 3
- 6
- 9
- 18
These are the only positive integers that divide 18 evenly.
To illustrate, consider the division:
| Divisor | Calculation | Result | Remainder |
|---|---|---|---|
| 1 | 18 ÷ 1 | 18 | 0 |
| 2 | 18 ÷ 2 | 9 | 0 |
| 3 | 18 ÷ 3 | 6 | 0 |
| 6 | 18 ÷ 6 | 3 | 0 |
| 9 | 18 ÷ 9 | 2 | 0 |
| 18 | 18 ÷ 18 | 1 | 0 |
Interpretation 2: Numbers That Are Evenly Divisible by 18 (Multiples of 18)
Multiples of 18 are numbers that you get when you multiply 18 by any integer (e.g., 1, 2, 3, 4, and so on). These numbers can be divided by 18 without leaving a remainder. Unlike factors, which are finite, the multiples of 18 are infinite.
Here are some examples of numbers that can be divided by 18:
- 18 (18 × 1)
- 36 (18 × 2)
- 54 (18 × 3)
- 72 (18 × 4)
- 90 (18 × 5)
- 108 (18 × 6)
- And so forth, extending infinitely in both positive and negative directions (e.g., -18, -36, -54).
Any number that is part of the 18 times table is a multiple of 18 and can therefore be divided by 18.
How to Identify Multiples of 18 (Divisibility Rules)
To determine if a larger number is divisible by 18, you can use divisibility rules. Since 18 is the product of 2 and 9 (its prime factors are 2 and 3 x 3), a number is divisible by 18 if and only if it meets both of the following conditions:
- Divisibility by 2: The number must be an even number. This means its last digit must be 0, 2, 4, 6, or 8.
- Divisibility by 9: The sum of its digits must be divisible by 9.
Example: Let's check if 576 is divisible by 18.
- Is it even? Yes, it ends in 6.
- Is the sum of its digits divisible by 9? 5 + 7 + 6 = 18. Since 18 is divisible by 9 (18 ÷ 9 = 2), 576 is also divisible by 9.
Since both conditions are met, 576 is divisible by 18 (576 ÷ 18 = 32).
