How to solve Divisibility Questions Quickly
A number is divisible by 3 if the sum of the digits of the number is divisible by 3. For example : 981 is divisible by 3 since the sum of the digits is 15
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How To Solve Divisibility Questions Quickly
How To Solve Divisibility Questions Quickly & Definition
- The capacity of a dividend to be exactly divided by a given number is termed as divisibility.
- One whole number is divisible by another if, after dividing, the remainder is zero.
- If the whole number is divisible by another number than the second number is factor of 1st number.
Type 1: Find the largest or smallest number
Question 1. What smallest number should be added to 1056 so that the number is completely divisible by 23?
Options
A. 2
B. 0
C. 1
D. 3
Solution On dividing 1056 by 23 we get remainder as 21
Required number = 23 – 21 = 2
1056 + 2 = 1058
1058 is completely divisible by 23 leaving reminder as 0.
Correct option:1
Question 2. In the given numbers, if first digit of each number is replaced by second digit, second digit is replaced by third digit, and third digit is replaced by first digit. Find out the second lowest number?
456 137 564 238 625
Options
A. 238
B. 625
C. 456
D. 137
Solution 456 137 564 238 625
On replacing the position as per the instructions given in the question, the number become
564 371 645 382 256
Therefore, the second lowest number is 137
Correct option:D
Question 3. Find the largest 4 digit number which is exactly divisible by 88?
Options
A. 9955
B. 9988
C. 9944
D. 9088
Solution Largest 4 digit number is 9999
On dividing 9999 by 88, remainder = 55
Required number = 9999 – 55 = 9944
Correct option:C
Type 2: Which of the following numbers is/or not divisible by given number.
Question 1. Which of these numbers is not divisible by 5?
Options
A. 345675
B. 234565
C. 230050
D. 345601
Solution A number is exactly divisible by 5 if it has the digits 0 or 5 at one’s place. Therefore, only option D is not divisible.
Correct option:4
Question 2. Which of these numbers is not divisible by 7?
Options
A. 875
B. 4143
C. 1470
D. 5488
Solution For 4143
Remove 3 from the number and double it = 6
Remaining number is 414, now subtract 414 from 6 = 414 – 6 = 408.
Repeat the process, We have last digit as 8, double = 16
Remaining number is 40, now subtract 40 from 16 = 40 – 16 = 24.
As 24 is not divisible by 7, hence the number 414 is not divisible by 7.
Correct option:B
Question 3. How many numbers between 300 and 900 are divisible by 4, 5 and 6?
Options
A. 10
B. 13
C. 14
D. 15
Solution First find the LCM of 4, 5, and 6 = 60
Now, on dividing 900 by 60 we get quotient as 15
On dividing 300 by 60 we get quotient as 5
Therefore the required number is 15 – 5 = 10
Correct option:A
Type 3: How To Solve Divisibility Questions Quickly.
Find the remainder
Question 1. On dividing a number by 60, we get 159 as quotient and 0 as remainder. On dividing the same number by 50, what will be the remainder?
Options
A. 40
B. 10
C. 20
D. 30
Solution Number = 159 * 60 + 0 = 9540
On dividing 9540 by 50 we get remainder as 40
Correct option:A
Question 2. What is the remainder when (2p + 2)2 is divided by 4 and ‘p’ is an integer?
Options
A. 1
B. 2
C. 3
D. None of the above
Solution On expanding (2p + 2)² = 4p² + 8p + 4
Now, take 4 common, then we get 4(p² + 2p + 1)
Let the value of p be 1
4 (12 + 2*1 + 1) = 16
Hence, 16 is divisible by 4 and the remainder will be 0
Correct option:4
Question 3. Find the remainder when 4875 is divided by 17.
Options
A. 19
B. 12
C. 21
D. 13
Solution Rem \frac{4 ^ {875}}{ 17}
Rem\frac{4 * 4 ^ {874}}{ 17}
Rem \frac{4 * 16 ^ {437}}{ 17}
as when 4 * (17-1)437 is divided by 17, it will give remainder of 4 * (-1)
Rem [4*\frac{(-1)}{ 17}]
Rem \frac{-4}{ 17}
= 13
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