Divisibility Test of 24

24 is one of the highest numbers with a divisibility rule. Mostly, people don’t opt for the divisibility rule of 24 but when they do, it becomes a lot easier than regular division.Divisibility rule if 24 helps in determining whether a number is completely divisible by 24 or not without actually following the traditional division method. The divisibility rule of 24 states that a number is divisible by 24 if it is divisible by both 3 and 8. Here, one should keep this in mind that both 3 and 8 should be an absolute divisor and not any one of them. If a number is not divisible by either 3 or 8, then it won’t be divisible by 24. This can be clearly understood with the help of examples given below.

 Example – 96

(i) Divide 96/3 = 32

(ii) Divide 96/8 = 12

Here, it can be clearly seen that 96 is divisible by both 3 as well as 8 which makes it divisible by 24.

Example- 104

(i) Divide 104/3 = Not completely divisible

(ii) Divide 104/8 = 13

Here , it can be seen that the number is divisible by 8 and not 3 . Hence, 104 is not divisible by 24.

Example- 99

(i) Divide 99/3 = 33

(ii) Divide 99/8 = Not completely divisible 

Here, in the above case , 99 is divisible by 3 but not 8 . Hence, it is not divisible by 24.

In order to understand the divisibility rule of 24 more easily and make the process of calculating it faster, one should have an in depth idea of divisibility rule of 3 and 8.

Divisibility Rule of 3- The divisibility rule of 3 is a bit more conditional than that of other numbers. Following are the conditions applicable for a number to be divisible by 3.

1. All the digits of the number are divisible by 3. For example- 369

3/3=1, 6/3+2, 9/3=3. Here, it can be seen that all the three digits of the number are individually divisible by 3 making the number 369 divisible by 3 altogether. This can be applied to any number and if all the digits are not divisible by 3, the number won’t be divisible by 3 as well. For example- 694. 6/3 = 2, 9/3 = 3 and 4/3 is not divisible . In the case of this number , the first two digits are divisible by 3 but the last one is not because of which the number is not divisible by 3.

2. If the sum of all the digits is divisible by 3. For example- 327

3+2+7 = 12

12/3 = 4

Since, the sum of all the digits of the number 327 is divisible by 3, the number is also divisible 3.

Divisibility Rule of 8- There are two conditions for a number to be divisible by 8. If any of the two conditions is fulfilled , the number would be considered to be divisible by 8.

(a)The number formed by the last three digits of the number to be tested should be divisible by 8. There are very large numbers and it’s not possible to test the whole number through the traditional division method. Hence , if the number formed by the last three digits of any number is divisible by 8, then in that case the whole number will be divisible by 8.

 For example- 3945424

424/8 = 56. Here the last three digits are divisible by 8 making the number 3945424 divisible by 8 as well.

(b)The last three digits of the number to be tested for divisibility should be 0.Any number irrespective of how many digits are there in it, should have at least three zeroes as its last three digits in order to be divisible by 8. This is one of the criteria of divisibility by 8. Although it’s not a compulsory one but is one of the conditions.

To sum up , 24 is a number that can be complicated when used for long division and its divisibility rule is a great alternative which can make the calculation process easier.

Conclusion

Mathematics is based on four core methods of calculation, addition, subtraction, division and multiplication. Division being one of the four is as important as the other three methods of calculation. The main focus behind the existence of the divisibility rule is the lengthy process of division in case of large numbers. In the case of small numbers with three or less than three digits, it’s easy to determine whether the number is divisible or not but  when it comes to large numbers , the same process becomes lengthy and time-consuming. Divisibility rule not just reduces time but makes it easier for a person to find results.