Tips and Tricks and Shortcuts for Divisibility

December 13, 2022

Tips and Tricks for Divisibility

The process of whether the given number is exactly divisible by another number without actually performing the operation of division is called the test of divisibility.In this Page Tips and Tricks for Divisibility is given.

Tips and Tricks for Divisibility

Tips and Tricks  and Shortcuts for Divisibility

The divisibility rule is the shorthand method of determining whether a number divisible by fixed divisor.

  • Rule for 2
    A number is divisible by 2 when the number ends with 0,2,4,6,8.
  • Rule for 3
    If the sum of digit is divisible by 3 than the number is divisible by 3.
  • Rule for 4
    If the last two digit is divisible by 4, than the number is divisible by 4.
  • Rule for 5
    Number is divisible by 5 if the last digit is 0 or 5.
  • Rule for 6
    A number is divisible by if number is divisible by 2 AND 3.
  • Rule for 7 : Double the last digit and subtract it from the remaining leading truncated number to check if the result is divisible by 7 until no further division is possible
  • Rule for 8
    If the last 3 number is divisible by 8 than the number is divisible by 8.
  • Rule for 9
    Same as divisibility of 3 but sum of digits is divide by 9 in place of 3
  • Rule for 10
    If the last digit is 0 than the number is divisible by 10.

Type 1:Find the largest or smallest number

Question 1. Find the smallest 4 digit number which is exactly divisible by 41?

Options.

A. 1000

B. 1023

C. 1025

D. 1012

Solution     Smallest 4 digit number is 1000

On dividing 1000 by 41, remainder = 16

Required number = 1000 + (41 – 16) = 1025

Correct option: C

Question 2. Find the Largest 3 digit number which is exactly divisible by 25?

                     Options.

                     A. 975

                     B. 905

                     C. 980

                     D. 950

Solution     Largest Three digit numbers is 999
                    On dividing 999 by 25, remainder = 24
                    Required number = 999 – 24 = 975
                    Correct option: A

Type 2:Which of the following numbers is/or not divisible by given number.

Question 1. Which of these numbers is divisible by 3?

Options.

A. 1003

B.  253

C. 1031

D. 1221

Solution     1003 = 1 + 0 + 0 + 3 = 4, 4 is not divisible by 3

253 = 2 + 5 + 3 = 10, 10 is not divisible by 3

1031 = 1 + 0 + 3 + 1 = 5, 5 is not divisible by 3

1221 = 1 + 2 + 2 + 1= 6, 6 is divisible by 3

Correct option: D

Question 2. Which of these numbers is not divisible by 10?

                     Options.

                     A. 1250

                     B. 1253

                     C. 1930

                     D. 1220

Solution      Last digit of 1253  is not 0 so it is not divisible by 10

                     Correct option: B

Type 3: Tips and Tricks to Solve Divisibility Questions.
Find the remainder

Question 1. Find out the remainder of \frac{2^{12}}{5}

Options.

A. 1

B. 2

C. 0

D. 3

Solution     Convert 2^{12} in multiple of 16  = 16 x 16 x 16
                    =2^{4}\times 2^{4}\times 2^{4}

Now divide each number by 5

On dividing 16 by 5 we get remainder as 1

Now, multiply all the remainders 1 x 1 x 1 = 1

                    Correct option: A

Question 2. Find out the remainder when 7^{4} is divided by 5.

                    Options.

                     A. 0

                     B. 4

                     C. 1

                     D. 2

Solution    Divide 7 by 5 Remainder will 2

                   2\times 2\times 2\times 2 = 16

                   Now divide 16 by 5

                   On dividing 16 by 5 we get remainder as 1

                   Correct option: C

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