Divisibility Tricks: Easy Ways to Tell If a Number is Divisible

In the world of mathematics, divisibility rules are like secret shortcuts that help us determine if one number can be divided evenly by another without actually performing the division. These rules are especially useful when working with large numbers or when trying to simplify fractions. In this guide, we'll explore some common divisibility tricks that can make your calculations a breeze.

Divisibility by 2

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

**Example:** 124 is divisible by 2 because the last digit, 4, is even.

Divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

**Example:** 321 is divisible by 3 because 3 + 2 + 1 = 6, and 6 is divisible by 3.

Divisibility by 4

A number is divisible by 4 if the last two digits are divisible by 4.

**Example:** 4512 is divisible by 4 because the last two digits, 12, are divisible by 4.

Divisibility by 5

A number is divisible by 5 if its last digit is 0 or 5.

**Example:** 545 is divisible by 5 because the last digit is 5.

Divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3.

**Example:** 312 is divisible by 6 because it is divisible by 2 (even last digit) and divisible by 3 (3 + 1 + 2 = 6, which is divisible by 3).

Divisibility by 9

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

**Example:** 729 is divisible by 9 because 7 + 2 + 9 = 18, and 18 is divisible by 9.

Divisibility by 10

A number is divisible by 10 if its last digit is 0.

**Example:** 1230 is divisible by 10 because the last digit is 0.

Putting It All Together: Examples

Let's test our divisibility knowledge with some examples:

Number	Divisible by 2?	Divisible by 3?	Divisible by 4?	Divisible by 5?	Divisible by 6?	Divisible by 9?	Divisible by 10?
1234	Yes	No	No	No	No	No	No
270	Yes	Yes	No	Yes	Yes	Yes	Yes
783	No	Yes	No	No	No	Yes	No
5400	Yes	Yes	Yes	Yes	Yes	Yes	Yes
999	No	Yes	No	No	No	Yes	No
1024	Yes	No	Yes	No	No	No	No
360	Yes	Yes	Yes	Yes	Yes	Yes	Yes
81	No	Yes	No	No	No	Yes	No
42	Yes	Yes	No	No	Yes	No	No
15	No	Yes	No	Yes	No	No	No

By using these divisibility tricks, you can quickly identify whether a number is divisible by a specific factor without resorting to long division. This can be a valuable tool in simplifying fractions, solving problems, and even just making calculations faster and easier.

Beyond Basic Divisibility

While the divisibility rules we've discussed are great for common factors, there are more advanced rules for other numbers. For instance:

• Divisibility by 7: Double the last digit and subtract it from the remaining number. If the result is divisible by 7, the original number is also divisible by 7.
• Divisibility by 11: Alternately add and subtract the digits of the number. If the result is divisible by 11, the original number is also divisible by 11.

Exploring these more complex rules can further enhance your understanding of number relationships and provide you with even more efficient tools for working with numbers.