# Divisible or Not? How to Determine If a Number is Divisible

Divisibility is an important concept in mathematics and is used in a wide range of applications. Understanding whether a number is divisible or not is a crucial step in many mathematical problems. In this article, we will discuss how to determine if a number is divisible and explore some of the rules that can help simplify this process.

Divisibility is the ability of a number to divide another number without leaving a remainder. If a number is divisible by another number, then it can be expressed as a product of that number and another integer. For example, 15 is divisible by 3 because 3 goes into 15 evenly five times. In contrast, 62 is not divisible by 11 because it cannot be expressed as a product of 3 and another integer.

## Divisibility Rules

There are many rules for determining whether a number is divisible by another number. Some of the most common rules are:

### Divisibility by 2

A figure is divisible by 2 if its last digit is even. For example, 24 is divisible by 2 because its last digit is 4, which is even.

### Divisibility by 3

A figure is divisible by 3 if the sum of its digits is divisible by 3. For example, 132 is divisible by 3 because 1 + 3 + 2 = 6, which is divisible by 3.

### Divisibility by 4

A figure is divisible by 4 if the number formed by its last two digits is divisible by 4. For example, 628 is divisible by 4 because 28 is divisible by 4.

### Divisibility by 5

A number is divisible by 5 if its last digit is either 0 or 5. For example, 75 is divisible by 5 because its last digit is 5.

### Divisibility by 6

A figure is divisible by 6 if it is divisible by both 2 and 3. For example, 54 is divisible by 6 because it is divisible by both 2 and 3.

### Divisibility by 9

A figure is divisible by 9 if the sum of its digits is divisible by 9. For example, 207 is divisible by 9 because 2 + 0 + 7 = 9, which is divisible by 9.

## Using Divisibility Rules

Divisibility rules can help simplify the process of determining whether a figure is divisible by another number. For example, if we want to determine whether 342 is divisible by 3, we can add the digits 342 to get 9. Since 9 is divisible by 3, we know that 342 is also divisible by 3. Similarly, if we want to determine whether 128 is divisible by 4, we can look at the last two digits (28) and see that they are divisible by 4. Therefore, we know that 128 is divisible by 4.

We will explore some common divisibility rules and provide examples of how to use them.

### Divisibility by 2

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). For example, 264 is divisible by 2 because its last digit is 4, which is even. However, 357 is not divisible by 2 because its last digit is 7, which is odd.

### Divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 153 is divisible by 3 because 1 + 5 + 3 = 9, which is divisible by 3. However, 268 is not divisible by 3 because 2 + 6 + 8 = 16, which is not divisible by 3.

### Divisibility by 4

A number is divisible by 4 if the figure formed by its last two digits is divisible by 4. For example, 836 is divisible by 4 because 36 is divisible by 4. However, 297 is not divisible by 4 because 97 is not divisible by 4.

### Divisibility by 5

A number is divisible by 5 if its last digit is either 0 or 5. For example, 45 is divisible by 5 because its last digit is 5. However, 123 is not divisible by 5 because its last digit is not 0 or 5.

### Divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3. For example, 732 is divisible by 6 because it is divisible by both 2 (the last digit is even) and 3 (the sum of digits is divisible by 3). However, 245 is not divisible by 6 because it is not divisible by 2 (the last digit is odd) or 3 (the sum of digits is not divisible by 3).

### Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9. For example, 234 is divisible by 9 because 2 + 3 + 4 = 9, which is divisible by 9. However, 817 is not divisible by 9 because 8 + 1 + 7 = 16, which is not divisible by 9.

Using these rules can help you quickly determine whether a figure is divisible by another number, without the need for long division. In practice, you can use these rules to make mental calculations or to quickly check if an answer is correct. By understanding these rules, you can save time and effort in solving mathematical problems.

## Conclusion

Divisibility is an important concept in mathematics and is used in a wide range of applications. Knowing whether a number is divisible or not can be crucial in solving mathematical problems. There are many rules for determining whether a figure is divisible by another number, and these rules can help simplify the process. By using divisibility rules, we can determine whether a number is divisible quickly and easily, without the need for long division or other more complicated methods.