[Maths Class Notes] on Divisibility Rules Pdf for Exam

The concept of division is tied with breaking something into many pieces. You share your sweets with your companions. You share bits of your favorite dishes at dinner with your friends and family. You begin with one amount and end up with little pieces.

To the extent that words are concerned, we will use three terms in this segment. In every division problem, you will have one number divided by another. The number you are breaking is known as the dividend. The solutions to your division problems are called quotients and remainders. Six divided by two gives you the rest of the three.

The shortcuts in mathematics help us to identify without performing the whole division method whether a given integer is divisible by a divisor by examining its digits. Prime factorization for a number can be determined for a number quickly by applying multiple divisibility rules. When an integer divides any number completely without leaving any remainder, it is known as the divisor of that number. Divisibility rules are helpful in finding factors and multiples without performing long divisions.

Importance of Factors

The numbers which when multiplied to a number give another number, these numbers are known as factors. Factors are important because when any number is divisible by another number, then all the factors of the other number are divisible by the number. For example, if a number is divisible by 10, then it is also divisible by 2 and 5.

Just Like Fractions

This segment will move directly into the fractions region since fractions are fundamentally an alternate method for composing a division problem. When you move into further developed math, you may even work out division problems that resemble fractions.

You will discover that the fraction 1/4 has an indivisible incentive from one (1) partitioned by four (4). As you work with decimals, you will rapidly find that 1 divided by 4 is 0.25. The division is even imperative to rates. The decimal 0.25 is equivalent to saying 25 percent. One fourth of a pie is 25 % of the complete pie.

Assume you’re at a stationery shop and you have to discover which bargain is better by utilizing divisibility rules. Suppose 2 pencils cost Rs 6 and in another store, 4 pencils cost Rs 8. Which bargain is better? In the first case, each pencil costs Rs 3. In the second case, each pencil costs Rs 2. We realize that the shop with 4 pencils that cost Rs 8 is the better solution.

Long Division Method

Long division is an approach to take care of division problems with real numbers. These are division problems that you can’t do in your mind.

How to Write it Down?

To start with, you need to record the problem in a long division group. The normal division problem resembles this:

Dividend ÷ Divisor = Quotient

To record this in long division place it would seem that this:

How about we attempt a genuinely straightforward example: 187 ÷ 11 =?

The first step is to put the problem into the long division group:

11 ÷ 187

The second step is to decide the smallest number to one side of the dividend, for this situation 187, which can be divided by 11. The number 1 is too little, so we take a gander at the first two numbers “18”. Since 11 can fit into the number 18, so we can use it.

In this way, we record how often 18 can be divided by 11. For this situation, the right response is 1. In the event that we attempted 2 which would be 22, which is greater than 18.

Next, we compose 11 underneath the 18 in light of the fact that 1 × 11 = 11. At that point, we subtract 11 from 18. This equals 7, which we record.

Since we have a digit 7 remaining, the problem isn’t done. We presently move the 7 down from the end of 187.
In this way, we decide how often 11 will go into 77. That is actually multiple times. We record the 7 by the 1 in the right response zone. We record 77 underneath the 77 in light of the fact that 7 × 11 = 77.
Now we subtract 77 from 77. The right answer is zero. We have completed the problem. 187 ÷ 11 = 17.

A Few Tips for Long Division

Write down a different table for the divisor before you begin the problem. For instance, if the divisor is 11 you record 11, 22, 33, 44, 55, 66, 77, 88, 99, and so forth. This can help you in avoiding mistakes.
Put a 0 in the left places of the remainder that you aren’t utilizing. Ensure you keep every one of your numbers arranged. Composing perfectly and keeping the numbers arranged can truly help you with making fewer mistakes.
Double check the problem with verification. When you have your answer, do the problem backwards by multiplication to check whether your solution is correct or not.
The following are a couple of more instances of long division. Endeavor to work through these problems yourself to check whether you get similar outcomes.

Divisibility Tests

You have purchased 1235 chocolates and need to disperse them in your class. In what manner will you know with what number to partition them without really playing out the activity of division?

The procedure of whether the given number is exactly divisible by another number without really working out the process of division is known as the test of divisibility. Being exactly divisible implies that on division there is no leftover portion left. For understanding the divisibility rules for any number we have to know its divisibility with numbers like 2, 3, 4, 5, 9, 10 and 11.

Divisibility Rules for the Numbers 2–11

The number	Divisibility Rule
Divisibility by 2	Even numbers or the numbers having an even number as their last digit are divisible by 2. Example: 0, 2, 4, 6, 8, 10, 12, 14, etc.
Divisibility by 3	In a number, if the sum of all digits is divisible by 3, it is also divisible by 3. Example: 3, 6, 9, 12, 15, 18, 21, etc.
Divisibility by 4	In a number, if the last two digits are divisible by 4, the number is divisible by 4. Numbers having 00 as their last digits are also divisible by 4. Example: 4, 8, 12, 16, 780, 70744, etc.
Divisibility by 5	The numbers that have either 0 or 5 in their last digits are all divisible by 5. Example: 25, 35, 45, 95, 105, 200, etc.
Divisibility by 6	The number which is divisible by both 2 and 3 is divisible by 6. Example: 12, 18, 60, etc.
Divisibility by 7	In a number, when the last digit is subtracted twice from the remaining digits and gives the multiple of 7, the number is divisible by 7. Example: 77, 42, 49, 70, etc.
Divisibility by 8	In a number, when the last three digits are divisible by 8, the number is divisible by 8. The numbers having 000 as their last digits are also divisible by 8. Example: 2000, 880, 805256, etc.
Divisibility by 9	In a number, when the sum of all digits is divisible by 9, the number is also divisible by 9. Example: 171, 99, 18, etc.
Divisibility by 10	In a number, when the last digit is 0, the numbers are all divisible by 10. Example: 12120, 110, 520, 440, etc.
Divisibility by 11	In a number, when the difference of the sums of the alternative digits is divisible by 11, the number is divisible by 11. Example: 1122, 814, 592845, etc.

Solved Examples

1. Which of the following numbers is divisible by 22?

(a) 4683

(b) 7106

(d) 5682

Solution:

For a number to be divisible by 22, it must be divisible both by 2 and 11. Since A and C are odd numbers, they are not divisible by 22.

In the case of D, (5 + 8) – (6 + 2) = 13 – 8 = 5, which is not a multiple of 11, so D is not divisible by 11, hence it is not divisible by 22.

Since B is an even number, it is divisible by 2. Also, (7 + 0) – (1 + 6) = 7 – 7 = 0, hence 7106 is divisible by 11. So, B is divisible by 22.

Hence the answer is B.

Engineering interview questions, Mcqs, Objective Questions,Class Notes,Seminor topics,Lab Viva Pdf free download. CIVIL | Mechanical | CSE | EEE | ECE | IT | Chemical Online Quiz Tests for Freshers.