DIVISIBILITY TEST- CBSE Mathematics
Divisibility Test :-
This topic contains the divisibility test by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 with examples for more understanding.
Divisibility Test by 2:-
· If unit digit of a number is even ( 0, 2, 4, 6, 8) then that number is divisible by “2”
· All even numbers are divisible by “2”.
Example 1:-
· Let given number is 258694
· Unit digit of this number is “4” it is even. Therefore 258694 is also divisible by “2”
Example 2:-
· Let given number is 2586947
· Unit digit of this number is “7”, it is odd. So the number 2586947 is not divisible by “2”.
DIVISIBILITY TEST- CBSE Mathematics
Divisibility Test by 3:-
· If sum of the digits of a given number is divisible by “3” then that number is also divisible by “3”.
Example 1:-
· Let given number is :-345897
· Sum of the digits: 3+4+5+8+9+7 = 36
· 36 is divisible by “3”, so 345897 is also divisible by “3”
Example 2:-
· Let given number is :- 985897
· Sum of the digits: 9+8+5+8+9+7 = 46
· 46 is not divisible by “3”, so 985897 is also not divisible by “3”
DIVISIBILITY TEST- CBSE Mathematics
Divisibility Test by 4:-
· Take last two digits of of a given number and divide it by “4”, if it is divisible by “4”, then the given number is also divisible by “4”.
· If last two digits of a given number is “00” then that number is also divisible by “4”.
Example 1:
· Let given number is 37984
· Last two digits : 8, 4, 84 is divisible by “4”. So 37984 is also divisible by “4”
Example 2:
· Let given number is 839842
· Last two digits : 4, 2, 42 is not divisible by “4”. So 839842 is also not divisible by “4”
Example 3:
· Let given number is 9739800
· Last two digits : 00 , yes 9739800 is also divisible by “4”
· If last digits of a given number is either “0” or “5” then the given number is also divisible by “5”.
Example 1:
· Let given numbers are 379520, 789735
· Last digit “0” and “5” . Yes above both numbers are divisible by 5
Example 2:
· Let given number is 379523
· Last digit “3” So above number is not divisible by 5
Divisibility Test by 6:-
· If a number is divisible by both “2” and “3” then that number is also divisible by 6.
Example 1:
Let given number is 357846
· Last digit is “6”, it is even. So it is divisible by “2”
· Sum of the digits: 3+5+7+8+4+6 = 33, “33” is divisible by “3”. So 357846 is also divisible by “3”
· Here we find that 357846 is divisible by both “2” and “3”. Hence 357846 is also divisible by “6”
DIVISIBILITY TEST- CBSE Mathematics
Divisibility Test 7:-
· Take last digit of a given number.
· Now subtract the double of this digit from the remaining number.
· Now see whether the result is divisible by "7" or not.
· If judgment is still difficult then repeat the above process again and again, till you left with two digit number then make the judgment.
Example 1:-
· Let given number is 21875
· Last digit “5”. Double of 5 is = 10
· Now find 2187-10 = 2177
· Last digit “7”. Double of “7” is = 14
· Now find 217 - 14 = 203
· Last digit “3”. Double of 3 is = 6
· Now find 20-6 = 14
· Since 14 is divisible by “7” so 21875 is also divisible by “7”
Example 2:
· Let given number is 789423
· Last digit “3”. Double of 3 is = 6
· Now find 78942 – 6 = 78936
· Last digit “6”. Double of 6 is = 12
· Now find 7893-12 = 7881
· Last digit “1”. Double of 1 is = 2
· Now find 788-2 = 786
· Last digit “6”. Double of 6 is = 12
· Now find 78-12 = 76
· 76 is not divisible by “7” so number 35789423 is not divisible by “7”
DIVISIBILITY TEST- CBSE Mathematics
Divisibility Test by 8:-
· Take last three digits of a given number and divide it by “8”, if it is divisible by “8” then the given number is also divisible by “8”.
Example 1:
· Let given number is : 5793512
· Last three digits : 5, 1, 2,
· 512 is divisible by “8” (512/8 = 64) so 5793512 is also divisible by “8”
Example 2:
· Let given number is : 5793515
· Last three digits : 5, 1, 5,
· 515 is not divisible by “8”, so 5793515 is also not divisible by “8”
DIVISIBILITY TEST- CBSE Mathematics
Divisibility Test by 9:-
· If sum of the digits of a given number is divisible by “9” then that number is also divisible by “9”.
Example 1:
· Let given number is : 63918
· Sum of the digits: 6+3+9+1+8 = 27
· 27 is divisible by “9”, so this number is also divisible by 9”
Example 2:
· Let given number is : 63925
· Sum of the digits: 6+3+9+2+5 = 25
· 25 is not divisible by “9”, so number 63925 is also not divisible by “9”
Divisibility Test by 10:-
· If last digits of a given number is “0” then the given number is also divisible by “10”.
Example 1:
· Let given number is : 63910
· Last digit is “0”, so 63910 is divisible by “10”
Example 2:
· Let given number is : 63917
· Last digit is “7” so 63917 is not divisible by “10”
DIVISIBILITY TEST- CBSE Mathematics
Divisibility Test by 11:-
· Mark the digits of a given number odd or even, starts from the right side (unit digit).
· Add the digits at odd position.
· Add the digits at even places.
· Find the difference between the two sums.
· If difference is either “0” or divisible by “11” then that number is also divisible by 11.
· If the difference is not divisible by 11 then that number is not divisible by 11.
Example 1:
· Let given number is : 659175
· Sum of the digits at even place = 7+9+6 = 22
· Sum of the digits at odd places = 5+1+5 = 11
· Difference: 22-11 = 11
· Since difference is divisible by “11” so the number 659175 is also divisible by “11”
Example 2:
· Let given number is : 959171
· Sum of the digits at even place = 1 + 1 + 5 = 7
· Sum of the digits at odd places = 7+9+9 = 25
· Difference: 25-7= 18
· Since difference”18” is not divisible by “11” so the number 959171 is not divisible by “11”
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