TESTS OF DIVISIBILITY
(f). Divisibility By 10 :
A number is divisible by 10 only when its unit digit is 0(zero).
Example : (1) 68720 is divisible by 10 because its unit digit is 0 .
(2) 29850 is divisible by 10 because its unit digit is 0.
(3) 687405 is not divisible by 10 ,since its unit digit is 5 not 0 .
(G). Divisibility by 5 :
A number is divisible by 5 only when its unit digit is 0 or 5 .
Example ; (1) 6785 is divisible by 5 because its unit digit is 5 .
(2) 96750 is divisible by 5 because its unit digit is 0 .
(H). Divisibility by 7,11,13 :
A number can be divisible by 7,11 or 13 if and only if the difference of the number formed by the last three digits and the number formed by the rest digits is divisible by 7,11 or 13 respectively .
Example ; check whether 139132 is divisible by 7 or not .
Solution; step (H.1)
number formed by the last three digits is 132 .
Step (H.2) : number formed by rest of digits is 139
Step (H.3) ; we take difference between these two numbers
139 - 132 = 7
Since the difference is divisible by 7 . Hence the given number is also divisible by 7.
(2) check whether 12478375 is divisible by 13 or not.
Solution; step1 . 12478 - 375 = 12103
Step 2. 12 - 103 = - 91
Since the difference is divisible by 13 .Hence the given number is divisible by 13 .
(3) check whether 29435417 is divisible by 11or not.
Solution ; step(1) 29435 - 417 = 29018
Step(2) 29 - 018 = 11
Since the difference is divisible by 11 so the number is also divisible by 11 .
(I). Divisibility by 11 :
A number is divisible by 11 if the difference between the sum of the digit at odd places and sum of digits at even places is equal to zero or a number divisible by 11.
Example ; check 29435417 is divisible by 11 or not .
Solution; step(1). Sum of its digits at odd places is
7+4+3+9 = 23
Step(2). Sum of its digits at even places is
1+5+4+2 = 12
Step (3). Difference between these two numbers is
23 - 12 = 11
Since difference is divisible by 11 .Hence the given number is also divisible by 11 .
(2). 57945822
(Sum of digit at odd places - sum of digits at even places)
(2+8+4+7) - ( 2+5+9+5) = 21 - 21 = 0
Since the difference is zero so the number is divisible by 11 .
(f). Divisibility By 10 :
A number is divisible by 10 only when its unit digit is 0(zero).
Example : (1) 68720 is divisible by 10 because its unit digit is 0 .
(2) 29850 is divisible by 10 because its unit digit is 0.
(3) 687405 is not divisible by 10 ,since its unit digit is 5 not 0 .
(G). Divisibility by 5 :
A number is divisible by 5 only when its unit digit is 0 or 5 .
Example ; (1) 6785 is divisible by 5 because its unit digit is 5 .
(2) 96750 is divisible by 5 because its unit digit is 0 .
(H). Divisibility by 7,11,13 :
A number can be divisible by 7,11 or 13 if and only if the difference of the number formed by the last three digits and the number formed by the rest digits is divisible by 7,11 or 13 respectively .
Example ; check whether 139132 is divisible by 7 or not .
Solution; step (H.1)
number formed by the last three digits is 132 .
Step (H.2) : number formed by rest of digits is 139
Step (H.3) ; we take difference between these two numbers
139 - 132 = 7
Since the difference is divisible by 7 . Hence the given number is also divisible by 7.
(2) check whether 12478375 is divisible by 13 or not.
Solution; step1 . 12478 - 375 = 12103
Step 2. 12 - 103 = - 91
Since the difference is divisible by 13 .Hence the given number is divisible by 13 .
(3) check whether 29435417 is divisible by 11or not.
Solution ; step(1) 29435 - 417 = 29018
Step(2) 29 - 018 = 11
Since the difference is divisible by 11 so the number is also divisible by 11 .
(I). Divisibility by 11 :
A number is divisible by 11 if the difference between the sum of the digit at odd places and sum of digits at even places is equal to zero or a number divisible by 11.
Example ; check 29435417 is divisible by 11 or not .
Solution; step(1). Sum of its digits at odd places is
7+4+3+9 = 23
Step(2). Sum of its digits at even places is
1+5+4+2 = 12
Step (3). Difference between these two numbers is
23 - 12 = 11
Since difference is divisible by 11 .Hence the given number is also divisible by 11 .
(2). 57945822
(Sum of digit at odd places - sum of digits at even places)
(2+8+4+7) - ( 2+5+9+5) = 21 - 21 = 0
Since the difference is zero so the number is divisible by 11 .
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