# Free Tutorial: Law of Divisibility in Mathematics

In this article, I am explaining one of the important concepts of mathematics i.e. law of divisibility. Different numbers are divisible by different numerals. You should find out if a particular numeral can be divided by a divisor. So, you should use some formulas to calculate and test the divisibility of a particular numeral by any divisor.

What is a divisor? A numeral to be divided by a certain number is a divisor. For example, if the fraction is 14/2, it means that 14 is to be divided by 2. Here, 2 is the divisor, and the numeral for division or dividend is 14. When you divide 14 by 2, the remainder is 0, and hence 14 is divisible by 2. Hence, the quotient is a whole number, i.e., 7. But you cannot divide 15 by 2, as you obtain 1 as the remainder. So, if you want to test if a particular number is divisible by any numeral, then you should use specific formulas or methods. In this article, I am explaining the divisibility of numbers 2, 3, 4, 5, 6, 8, 10, 11, and 25.

## Ways to test divisibility for different numbers

### How to test divisibility of 2

Any even number is divisible by 2, such as 4, 6, 8, 10, 12, 16, etc. So, if you want to test the divisibility of 2, then you should simply see that the last number, or the number in one's position, ends with 2, 4, 6, 8, or 0. The number in the unit or one's position should be an even number. For example, the number 142386 is divisible by 2 as the value of one's position is 6. But the numeral 14265 is not divisible by 2 as the value of one's position is 5, an odd number.

### Testing divisibility of 3

To test if a number is divisible by 3, you should add the numerals, and if the answer obtained can be divided by 3 without a remainder, then it is divisible by 3. For example, the number 1533 is divisible by 3 because if you add 1 + 5+3+3, the answer obtained is 12, and you can further add 1+2 which is equivalent to 3. So, 3 is divided by its own number, 3. Is the number 164 divisible by 3? So, you should add 1 + 6 + 4, and the answer is 11. So, when you further add 1 + 1, then you get 2, which is not divisible by 3. So, the number is not divisible by 3.

### Test of divisibility of 4

If the last two digits of a number can be divided by 4 without obtaining a remainder, then it is divisible by 4. For example, the number 2408 is divisible by 8 as the last two digits, 08, can be divided by 4. As you know, 4 x 2 is 8, and hence it is divisible by 4. But the number 2345 is not divisible by 4. The last two digits of a number are 45, and they are not divisible by 4.

### Test of divisibility of number 5

If the last digit of a number is 5 or 0, it is divisible by 5, e.g., 15, 30, 50, 55, etc. If you want to test if 53210 is divisible by 5, you should simply see the last digit, which is 0, and hence it is divisible by 5. But the number 23419) is not divisible by 5, as the last digit, or the position of one's place, is 9.

### Test of divisibility of number 6

As you know, 2 x 3 is 6, so a number should be divisible by 2 and 3. For example, if you want to test the divisibility of the number 6600, you should first find the divisibility of 2. The last digit is 0, an even number, and hence it is divisible by 2. It is also divisible by 3 as the sum of 6+6+0+0 is 12. So, it is divisible by 6. But the number 650 is not divisible by 6 as it cannot be divided by 3. If you add 6 and 5, then you obtain 11, and 11 is not divisible by 3. It is divisible by 2, but not by 3.

### Test of divisibility of 8

When the last three digits of a numeral can be divided by 8, then it is divisible by 8. For example, if the number is 4888, then the last three numbers, '888, can be divided by 8.

### Test of divisibility of 10

How do you know if a number is divisible by 10? The last digit of a number should be 0, simply. For example, the last digit of 143260 is 0, and hence it is divisible by 10.

### Test of divisibility of 11

To test the divisibility of 11, first add the digits at odd places. Then add the digits at even places. If the answer obtained after subtraction is 0 or 11, then it is divisible by 11. For example, if the number is 86416, then add 8 + 4+ 6, and the answer is 18. Then add numbers 6 + 1, and the answer is 7. If you subtract 7 from 18, you get 11. So, the number is divisible by 11.

### How to test divisibility by 25?

If the last two digits of a number can be divided by 25, then the number is divisible by 25. For example, if the number is 650, it is divisible by 25 as the last two digits are divisible by 25. If you divide 650 by 25, the answer is 26.

Author: Umesh21 Apr 2023 Member Level: Diamond   Points : 3

I request the author to check the first line of the article where it is not clear as what is a divisor. Actually a number which is to be divided is called dividend (14 in the example given) and a number which divides the dividend is called divisor (2 in the case). Please correct the first sentence accordingly.
The article has given very good tips for ascertaining the divisibility by certain divisors. It would be very useful for the students as a quick method to check the divisibility.
In Mathematics there are tips and tricks in many topics and if we use them then the Mathematics subject becomes an interesting subject to study and then to learn its intricacies. For example, to find the curved surface area of a hollow cylinder we can simply imagine to cut it vertically on one side and spread it and it becomes a rectangle and we can easily find the curved surface area which is same as that of the rectangle.

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