Efficient Methods to Determine if a Number is Divisible by 24- A Comprehensive Guide

How to Check if a Number is Divisible by 24

Divisibility is a fundamental concept in mathematics that helps us understand the relationship between numbers. One of the most common questions that arise is how to check if a number is divisible by 24. In this article, we will explore the methods and steps to determine if a given number is divisible by 24.

Firstly, it is important to note that a number is divisible by 24 if it is divisible by both 3 and 8, as 24 is the product of these two prime numbers (24 = 3 × 8). Therefore, to check if a number is divisible by 24, we need to ensure that it is divisible by both 3 and 8.

Here are the steps to check if a number is divisible by 24:

1. Check Divisibility by 3:
To determine if a number is divisible by 3, add up all the digits of the number. If the sum is divisible by 3, then the original number is also divisible by 3. For example, let’s check if 123456 is divisible by 3:
Sum of digits = 1 + 2 + 3 + 4 + 5 + 6 = 21
Since 21 is divisible by 3, we can conclude that 123456 is divisible by 3.

2. Check Divisibility by 8:
To check if a number is divisible by 8, examine the last three digits of the number. If these three digits form a number that is divisible by 8, then the original number is also divisible by 8. For instance, let’s check if 123456 is divisible by 8:
Last three digits = 456
Since 456 is divisible by 8 (456 ÷ 8 = 57), we can conclude that 123456 is divisible by 8.

3. Conclusion:
If a number is divisible by both 3 and 8, it is divisible by 24. In our example, 123456 is divisible by both 3 and 8, so it is divisible by 24.

In summary, to check if a number is divisible by 24, follow these steps:
– Check if the number is divisible by 3 by adding up its digits.
– Check if the number is divisible by 8 by examining its last three digits.
– If the number is divisible by both 3 and 8, it is divisible by 24.

By following these steps, you can easily determine if a given number is divisible by 24.