How can you easily tell if a large number will be divisible by 24?
The number 24 is made up of the factors of 3 and 8. This is an important feature because you should know that you can easily determine if a number is divisible by 3 and 8.
How To Tell If A Number Is Divisible By 8
Similar to my previous article in determining if a number is divisible by 4 the process is somewhat the same for determining if a number is divisible by 8 as multiples of 8 repeat themselves at every 1,000.
Therefore, just as the number 4 repeats itself at every 100 you could take any large number and look at the large three digits and if they are divisible by 8 then the whole number is divisible by 8.
But to take this a step further in determining whether a number is divisible by 24 you need to similarly check if the large number is divisible by 3 .
Therefore, do you quick divisible by 8 check first and then do your second check by adding up all the numbers and seeing if that sum is divisible by 3.
If both conditions are satisfied then the number is divisible by 24.
Let’s try it using an example:
Is the number 62,472 divisible by 24?
Step 1: get the last 3 digits and see if they are divisible by 8?
472 divided by 8 is divisible by 8, proceed to step 2.
Step 2: add up all the digits to see if they are divisible by 3
6 + 2 + 4 + 7 + 2 = 21
21 is divisible by 3.
Therefore you can conclude that 62,472 is divisible by 24, which it is – 2,603 times.
Try the process yourself, pick a random 5 or 6 digit even number and see if you can quickly find out if the number you’ve randomly chosen is divisible by 24.
The Product Of 4 Consecutive Numbers
One other interesting factoid about numbers being divisible by 24 is that the product of four consecutive integers themselves all divisible by 24.
This is easy to understand as four consecutive integers will be divisible by 2, 3 and 4, and the product of 2, 3 and 4 is itself 24.
Try it.
Think of 4 consecutive integers and divide it by 24: a whole number!
Summary
To determine if a number is divisible by 24 see if the last three digits are divisible by 8, if so then count up all the digits of the number and if this is divisible by 3 then the number is divisible by 24 .