Divisibility Test of 5

Meaning of Divisibility Rule

One should know what is divisibility before getting into the depths of the divisibility rule. In the process of  division, there are four components. First is the dividend, the number which is going to be divided. Second is the divisor, the number which dividend is divided. This is the quotient which is the result of division and fourth is the remainder which comes only when the number is not completely divided by its divisor. Division applies everywhere irrespective of the length of the number and so does the divisibility rule.

Divisibility rule is a non-calculative process of mathematics used to determine whether a number is divisible by its divisor or not. It can be used in case of large as well as small numbers and reduces the time and efforts of division.

Divisibility Rule of 5

As stated above, the divisibility rule is a process to check whether a number is divisible by its divisor or not without involving any calculation process. Many numbers have different divisibility rules which can be quite complicated and tricky but unlike those numbers , the divisibility rule of 5 is simple and easily understandable. According to the divisibility rule of 5, a number is divisible by 5 in the following cases :-

1. When the digit at unit’s place is 0- If any number irrespective of the digits in it, has 0 at its unit’s pace, then the number is divisible by 5. This can be checked by taking a number into consideration.

For example- 46890 is a number which has 0 at its unit place which makes it divisible by 5.

2. The digit at the unit place is 5- No matter how many digits are there in a number, if the last digit is 5 , the number is divisible by 5.This can be checked through the number 435 which has 5 as its unit digit making it divisible by 5.

Examples of numbers with divisibility rule of 5-

1. 15- this number has 5 as its unit digit making it divisible by 5. Also there is one thing to observe that 15 is a multiple of 5. Hence, one should always keep in mind that every number that is a multiple of that number is also a factor of the same number.

2. 680- In case of this number, the last digit is 0 and not 5 but as stated above, any number that has 0 as its last digit will be divisible by 5 as well. Henc, 680 is divisible by 5.

3. 460000-  In the case of this 6 digit number, the last number is 0 and it is divisible by 5 as well.

Divisibility rule in common for 5 and 10

The divisibility criteria of numbers is mostly unique in each case but sometimes it clashes and it is possible for a number to be divisible by more than one than number. This actually happens in the case of 5 and 10 , where a number is divisible by both 5 and 10 if it has 0 as its last digit. This can be understood by an example.

Example: 645430- this is a large number with 6 digits and will need long division but with the application of divisibility rule, one can deduce that the number is divisible by as well 10 because it has 0 as its unit digit. This is part of basic mathematics and will not be considered as a contradiction . This number is divisible by 2 as well because the criteria of 0 as units digit is applicable with 2 as well.

On the other hand , if one observes a number , for example, 79685 which is also divisible by 5 but it is not divisible by either 10 or 2 because there is no 0 at the unit place.

Divisibility rules of some other numbers

• Divisibility rule of 1-  1 is a number that can divide any existing number irrespective of the number of digits it has.

• Divisibility rule of 2- ALL  the even numbers are divisible by 2, that’s why they are called even numbers. These numbers have 2,4m6m8 and 0 as their unit digit. A number that is divisible by 2 , becomes one- half of itself after division .

For example- 84/2 = 42. This number is completely divisible by 2 as it has 4 as its last digit.

• Divisibility rule of 3-  The number 3 has various criteria for divisibility as given below

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

3/3=1, 6/3=2, 9/3=3. Since, all the 3 digits are divisible by 3 , the number 369 is also divisible by 4.

2. If the sum of all the digits are divisible by 3. A number is an absolute factor of 3 if the sum of its digits are divisible by 3. For example- 327

3+2+7= 12

12/3= 4

The sum of the digits of 327 is 12 which is divisible by 3 making the whole number divisible by 3.

• Divisibility Rule of 4- The divisibility rule of 4 is a bit different and tricky as compared to other numbers.A number is said to be divisible by 4 if the number formed by the last two digits of the number is divisible by 4. It is suggested to understand the rule through the given example-

Example- 2684

The first two digits of the given number are 8 and 4 and the number formed is 84 whichThe set 2 di is divisible by 4. Hence , the number 2684 is also divisible by 4.

Many numbers have many divisibility criteria but in case it’s less and simple. Also , the criterias of many numbers do match but that is not a contradiction. The article has given an easy explanation of the divisibility rule of 5 for the convenience of the students 

Conclusion

Mathematics seems a complicated subject to a large number of students. There are many reasons for the same, such as a large number of formulas, fear of numbers or lack of concepts . But the most common reason is lengthy calculations. At first, one feels that calculations are complicated but after understanding the process,it becomes easy and mundane which bores a person. Divisibility rule is a solution to this problem where one can determine whether a number is divisible or not without picking up pen and paper.