Thursday, 8 June 2017

Number System IV – Divisibility Rules to solve Number System Questions

In this post, we will discuss divisibility rules of the numbers which will help you solve Number System Questions in less time to crack SBI PO, IBPS PO and SSC CGL Exam.
Divisibility Rules
Number System Questions that are asked in IBPS PO and SSC CGL Exam are complex and time-consuming. But if you know the divisibility rules of numbers, then you can solve number system questions in less than 10 seconds in IBPS PO and SSC CGL Exam in less time.
In this post, we have discussed divisibility rules of all the possible numbers which will help you solve number system questions as quickly as possible and thus save your time during IBPS PO and SSC CGL Exam. 
Divisibility Rules
                                           
Divisibility Rules to solve Number System Questions in IBPS PO and SSC CGL Exam
Number
Rule of Divisibility
Example
Testify
2
The number should be even.
2796
2796 is divisible by 2.
3
The sum of the digits should be a multiple of 3.
689154
6 + 8 + 9 + 1 + 5 + 4 = 33 689154 is divisible by 3 as 33 is a multiple of 3.
4
The number formed by the last two digits of a number should be a multiple of 4
389416
As 16 is the multiple of 4, 389416 is divisible by 4.
5
The last digit of the number should be ‘0’ or ‘5’
18975
18957 is divisible 5 as the last digit of the number is 5.
6
The number should be divisible by 2 and 3.
918654
2 – The number is divisible by 2 as it as an even number.
 3- The number is divisible by 3 as the sum of its digits is 33.
 6- Therefore the number is divisible 6 as it is divisible by 2 and 3.
8
The number formed by the last three digits of the number should be a multiple of 8
13840
As 840 is a multiple of 8, 13840 is divisible by 8.
9
The sum of the digits of the number should be a multiple of 9.
9516348
9 + 5 + 1 + 6 + 3 + 4 + 8 = 36.
As 36 is a multiple of 9, 9516348 is divisible by 9.
10
The last digit of the number should be 0
495320
As the last digit of the number is 0, 495320 is divisible by 10.
11
The difference between the sums of digits at alternate positions should be 0 or a multiple of 11.
64738223
6 + 7 + 8 + 2 – 4 + 3 + 2 + 3 = 23 – 12 = 11. Therefore, the number is divisible by 11 as the difference between the sums of the digit at alternate position is multiple of 11.
12
The number should be divisible by both 3 and 4.
13764
3 ; 1 + 3 + 7 + 6 + 4 = 21 4; the number is divisible by 4 as the last two digit i.e. 64 is a multiple of 4. 12 ; The number is divisible by 12 as the number is divisible 3 and 4.


Divisibility Rule of 7 and 19

Divisibility Rule of 7
To check whether a number is divisible by 7 or not, the unit place of the number is separated from the rest of the number and multiplied with two and then it is subtracted from the rest of the number till we get a one or two digit number from which we can obtain that the number is a multiple of 7 or not.

Example: Number System Questions Solved using Divisibility Rule

Question: Is the number 224 a multiple of 7 or not?

Step 1: 224, the numbers we get after separation are 22 and 4

Step 2: Multiply the unit digit with 2
2 x 4 = 8

Step 3: subtract the number from the rest of the number.
22 – 8 = 14

Step 4: As 14 is a multiple of 7, we can denote that 224 is divisible by 7.

Divisibility Rule of 19

To check whether a number is divisible by 19 or not, the unit place of the number is separated from the rest of the number and multiplied with two and then it is added from the rest of the number till we get a two or three digit number from which we can obtain that the number is a multiple of 19 or not.

Example: Number System Questions Solved using Divisibility Rule

Question: Is the number 399 a multiple of 19 or not?

Solution:
Step 1: 399, the numbers we get after separation are 39 and 9

Step 2: Multiply the unit digit with 2
9 x 2 = 18

Step 3: Add the number to the rest of the number.
39 +18 = 54

Step 4: As 54 is a multiple of 19, we can denote that 399 is divisible by 19.

Divisibility Rule for Other Numbers in General

Above, we have seen divisibility rule of first 12 numbers and few special cases. Now we will check the divisibility rule of some general numbers.

Let's check the divisibility rule for the numbers such as 14, 15, 18, etc. 

To check the divisibility rule for other natural numbers we need to understand the concept of co-prime.

Co- Primes: Co-Primes are the numbers which have the highest common factor as 1.
For example:

Divisibility Rules

As we have seen the divisibility rule for the 12, is that the number should be a multiple of 3 and 4. It is as such because the number 3 and 4 are co-primes.
Divisibility Rules



Likewise, for other numbers we need to find their co-prime factors and therefore that’s how we can check the divisibility rule for other numbers.

Example: 18 – For the number 18, the number should be a multiple of 2 and 9 as they are co-primes.
Divisibility Rules




Example: Number System Questions Solved using Divisibility Rule

Question: What is the Smallest Number that should be added to 89357 to make it divisible by 9.
1)1           2) 3             3)4          4)7              5) None of these

Solution:
Smart Method:
Step 1:
We know that a number is divisible by 9 only when all the number sum up to be multiple of 9 
Now let’s add all the number to check whether this number is divisible by 9 or not.
8 + 9 + 3 + 5 + 7 = 32

Step 2:
Add a number to the 32 so that it becomes a multiple of 9.
As we need to add the smallest digit to the number so that it becomes a multiple of 9.
32 + 4 + 36
Hence, we need to add 4 to 89357 to make it a multiple of 9.

Therefore, the correct answer is option 3: 4
Divisibility Rules
Example: Number System Questions Solved using Divisibility Rule

Question:
What is the smallest digit that should be replaced by '*' in the number 296*12,  to make it divisible by 12?
1) 1              2) 2                3) 3                      4) 4              5) None of these
Solution:

Step 1:
To divisibility rule of 12 is that a number should be divisible by 4 and 3.
4 – The number is divisible by 4 as its last two digits end with 12 and 12 is the multiple of 4.
3 – To make a number divisible by 3 we need to add all its digits and the sum should be a multiple of 3.
2 + 9 + 6 + * + 1 + 2 = 20 + *

To make the sum a multiple of 3 we need to add 1 to it.
So, 20  1 = 21 and hence 1 is the smallest number that should be placed instead of * to make it divisible by 12.

Therefore, the answer is Option 1: 1.

Number System Questions for Practice on Divisibility Rules

Question: Which of the following numbers are divisible by 2, 5 and 9?
a) 149          b) 19400       c) 720345        d) 125370        e) 300000

Question: If the number 54872a63b1 divisible by 11 and 3 what will be the possible values for 'b' and 'a' respectively?
a) 1,6         b) 2,8             c) 3,9         d) 2,9             e) 1,7

Do drop your answers in the comment section!

Stay tuned for more Number System Questions.
Divisibility Rules
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