1. Check whether 9603 is divisible by 33 or not?Solution:Divisibility rule of 33 :
10 times the last digit and add it to the rest of the number.
If the answer is divisible by 33, then number is also divisible by 33.
(Apply this rule to the answer again if necessary)
`960color{red}{3}=>960 + color{red}{3} xx 10 = 960 +30 = 990`
`99color{red}{0}=>99 + color{red}{0} xx 10 = 99 = 99`
Here 99 is divisible by 33.
`:.` 9603 is divisible by 33.
Method-2 : Divisibility rule of 33 :
If number is divisible by 3 and 11, then number is also divisible by 33.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 9603 is `9+6+0+3=18`, which is divisible by 3.
`:.` 9603 is divisible by 3.
Divisibility rule of 11 :
Subtract the last digit from the rest of the number.
If the answer is divisible by 11, then number is also divisible by 11.
(Apply this rule to the answer again if necessary)
`960color{red}{3}=>960 - color{red}{3} = 957`
`95color{red}{7}=>95 - color{red}{7} = 88`
Here 88 is divisible by 11.
`:.` 9603 is divisible by 11.
Method-2 : Divisibility rule of 11 :
(Sum of digits in odd positions) - (Sum of digits in even positions) is 0 or divisible by 11, then number is also divisible by 11.
Sum of digits in odd positions : `6+3=9`
Sum of digits in even positions : `9+0=9`
Difference `=9-9=0`
which is divisible by 11.
`:.` 9603 is divisible by 11.
9603 is divisible by 3 and 11.
`:.` 9603 is divisible by 33.
2. Check whether 10989 is divisible by 33 or not?Solution:Divisibility rule of 33 :
10 times the last digit and add it to the rest of the number.
If the answer is divisible by 33, then number is also divisible by 33.
(Apply this rule to the answer again if necessary)
`1098color{red}{9}=>1098 + color{red}{9} xx 10 = 1098 +90 = 1188`
`118color{red}{8}=>118 + color{red}{8} xx 10 = 118 +80 = 198`
`19color{red}{8}=>19 + color{red}{8} xx 10 = 19 +80 = 99`
Here 99 is divisible by 33.
`:.` 10989 is divisible by 33.
Method-2 : Divisibility rule of 33 :
If number is divisible by 3 and 11, then number is also divisible by 33.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 10989 is `1+0+9+8+9=27`, which is divisible by 3.
`:.` 10989 is divisible by 3.
Divisibility rule of 11 :
Subtract the last digit from the rest of the number.
If the answer is divisible by 11, then number is also divisible by 11.
(Apply this rule to the answer again if necessary)
`1098color{red}{9}=>1098 - color{red}{9} = 1089`
`108color{red}{9}=>108 - color{red}{9} = 99`
Here 99 is divisible by 11.
`:.` 10989 is divisible by 11.
Method-2 : Divisibility rule of 11 :
(Sum of digits in odd positions) - (Sum of digits in even positions) is 0 or divisible by 11, then number is also divisible by 11.
Sum of digits in odd positions : `1+9+9=19`
Sum of digits in even positions : `0+8=8`
Difference `=8-19=-11`
which is divisible by 11.
`:.` 10989 is divisible by 11.
10989 is divisible by 3 and 11.
`:.` 10989 is divisible by 33.
3. Check whether 11814 is divisible by 33 or not?Solution:Divisibility rule of 33 :
10 times the last digit and add it to the rest of the number.
If the answer is divisible by 33, then number is also divisible by 33.
(Apply this rule to the answer again if necessary)
`1181color{red}{4}=>1181 + color{red}{4} xx 10 = 1181 +40 = 1221`
`122color{red}{1}=>122 + color{red}{1} xx 10 = 122 +10 = 132`
`13color{red}{2}=>13 + color{red}{2} xx 10 = 13 +20 = 33`
Here 33 is divisible by 33.
`:.` 11814 is divisible by 33.
Method-2 : Divisibility rule of 33 :
If number is divisible by 3 and 11, then number is also divisible by 33.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 11814 is `1+1+8+1+4=15`, which is divisible by 3.
`:.` 11814 is divisible by 3.
Divisibility rule of 11 :
Subtract the last digit from the rest of the number.
If the answer is divisible by 11, then number is also divisible by 11.
(Apply this rule to the answer again if necessary)
`1181color{red}{4}=>1181 - color{red}{4} = 1177`
`117color{red}{7}=>117 - color{red}{7} = 110`
`11color{red}{0}=>11 - color{red}{0} = 11`
Here 11 is divisible by 11.
`:.` 11814 is divisible by 11.
Method-2 : Divisibility rule of 11 :
(Sum of digits in odd positions) - (Sum of digits in even positions) is 0 or divisible by 11, then number is also divisible by 11.
Sum of digits in odd positions : `1+8+4=13`
Sum of digits in even positions : `1+1=2`
Difference `=2-13=-11`
which is divisible by 11.
`:.` 11814 is divisible by 11.
11814 is divisible by 3 and 11.
`:.` 11814 is divisible by 33.
4. Check whether 8641 is divisible by 33 or not?Solution:Divisibility rule of 33 :
10 times the last digit and add it to the rest of the number.
If the answer is divisible by 33, then number is also divisible by 33.
(Apply this rule to the answer again if necessary)
`864color{red}{1}=>864 + color{red}{1} xx 10 = 864 +10 = 874`
`87color{red}{4}=>87 + color{red}{4} xx 10 = 87 +40 = 127`
`12color{red}{7}=>12 + color{red}{7} xx 10 = 12 +70 = 82`
Here 82 is not divisible by 33.
`:.` 8641 is not divisible by 33.
Method-2 : Divisibility rule of 33 :
If number is divisible by 3 and 11, then number is also divisible by 33.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 8641 is `8+6+4+1=19`, which is not divisible by 3.
`:.` 8641 is not divisible by 3.
Hence 8641 is also not divisible by 33.
5. Check whether 11117 is divisible by 33 or not?Solution:Divisibility rule of 33 :
10 times the last digit and add it to the rest of the number.
If the answer is divisible by 33, then number is also divisible by 33.
(Apply this rule to the answer again if necessary)
`1111color{red}{7}=>1111 + color{red}{7} xx 10 = 1111 +70 = 1181`
`118color{red}{1}=>118 + color{red}{1} xx 10 = 118 +10 = 128`
`12color{red}{8}=>12 + color{red}{8} xx 10 = 12 +80 = 92`
Here 92 is not divisible by 33.
`:.` 11117 is not divisible by 33.
Method-2 : Divisibility rule of 33 :
If number is divisible by 3 and 11, then number is also divisible by 33.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 11117 is `1+1+1+1+7=11`, which is not divisible by 3.
`:.` 11117 is not divisible by 3.
Hence 11117 is also not divisible by 33.
6. Check whether 12152 is divisible by 33 or not?Solution:Divisibility rule of 33 :
10 times the last digit and add it to the rest of the number.
If the answer is divisible by 33, then number is also divisible by 33.
(Apply this rule to the answer again if necessary)
`1215color{red}{2}=>1215 + color{red}{2} xx 10 = 1215 +20 = 1235`
`123color{red}{5}=>123 + color{red}{5} xx 10 = 123 +50 = 173`
`17color{red}{3}=>17 + color{red}{3} xx 10 = 17 +30 = 47`
Here 47 is not divisible by 33.
`:.` 12152 is not divisible by 33.
Method-2 : Divisibility rule of 33 :
If number is divisible by 3 and 11, then number is also divisible by 33.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 12152 is `1+2+1+5+2=11`, which is not divisible by 3.
`:.` 12152 is not divisible by 3.
Hence 12152 is also not divisible by 33.
This material is intended as a summary. Use your textbook for detail explanation.
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