Amazing Number Divisibility Tricks: Mastering Quick and Easy Division

Divisibility tricks are essential tools for anyone looking to enhance their mathematical skills. These simple rules can help you quickly determine if a number can be divided by another without performing complex calculations. In this article, we will explore some amazing divisibility tricks that can streamline your calculations and improve your efficiency in mathematics.

Dividing by 2

The first and possibly the simplest divisibility trick is determining if a number is divisible by 2. All even numbers are divisible by 2. This includes any number ending in 0, 2, 4, 6, or 8. For example, the number 124 is even, and therefore, divisible by 2.

Dividing by 3

To check if a number is divisible by 3, add up all the digits in the number and see if the sum is divisible by 3. This method is particularly useful for larger numbers. As an example, take 12123: 1 2 1 2 3 9. Since 9 is divisible by 3, 12123 is also divisible by 3.

Dividing by 4

Another useful divisibility trick is checking if the last two digits of your number are divisible by 4. If they are, then the entire number is too. For example, in 358912, the last two digits are 12, which is divisible by 4. Therefore, 358912 is divisible by 4.

Dividing by 5

A quick and easy way to check divisibility by 5 is to see if the number ends in 5 or 0. For instance, 155 and 200 are both divisible by 5. This rule is straightforward and can be applied immediately.

Dividing by 6

To determine if a number is divisible by 6, first check if it is divisible by both 2 and 3. If it is, then it is also divisible by 6. This rule combines the previous two to simplify the process. The number 126, for example, is divisible by both 2 and 3, and thus, it is also divisible by 6.

Dividing by 7: Two Quick Tests

Dividing by 7 can be a bit more challenging, but with these two tests, you can make the job easier. The first method involves taking the last digit of the number, doubling it, and subtracting it from the rest of the number. If the result is divisible by 7, then the original number is too. For instance, in 357, doubling 7 gives 14. Subtracting 14 from 35 gives 21, which is divisible by 7, meaning 357 is also divisible by 7.

Test 2: For larger numbers, multiply each digit starting from the right (the ones place) by a sequence of 1, 3, 2, 6, 4, 5, and repeat as necessary. Add the products, and if the sum is divisible by 7, then so is the original number. As an example, to check if 2016 is divisible by 7, multiply 6 by 1 to get 6, 1 by 3 to get 3, 0 by 2 to get 0, and 2 by 6 to get 12. Adding these up (6 3 0 12) gives 21, which is divisible by 7. Therefore, 2016 is also divisible by 7.

Dividing by 8

Dividing by 8 can be simpler if you focus on the last three digits of the number. If the last three digits are divisible by 8, then the entire number is divisible by 8 as well. As an example, in 6008, the last three digits 008 are divisible by 8, so 6008 is also divisible by 8.

Dividing by 9

Similar to the divisibility rule for 3, the sum of the digits of a number should be checked for divisibility by 9 if you want to see if the entire number is divisible by 9. For instance, in 43785, the sum of the digits is 27 (4 3 7 8 5), and since 27 is divisible by 9, it follows that 43785 is also divisible by 9.

By mastering these divisibility tricks, you can improve your speed and accuracy in mathematical calculations. Whether you are a student, a teacher, or someone who deals with numbers regularly, these techniques can be invaluable tools for your work and studies.