1. Check whether 22704 is divisible by 88 or not?Solution:Divisibility rule of 88 :
If number is divisible by 8 and 11, then number is also divisible by 88.
Divisibility rule of 8 :
The last three digit is divisible by 8, then number is also divisible by 8.
Last 3 digit of 22704 is 704, which is divisible by 8.
:. 22704 is divisible by 8.
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)
2270color{red}{4}=>2270 - color{red}{4} = 2266226color{red}{6}=>226 - color{red}{6} = 22022color{red}{0}=>22 - color{red}{0} = 22Here 22 is divisible by 11.
:. 22704 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 :
2+7+4=13Sum of digits in even positions :
2+0=2Difference
=2-13=-11which is divisible by 11.
:. 22704 is divisible by 11.
22704 is divisible by 8 and 11.
:. 22704 is divisible by 88.
2. Check whether 30448 is divisible by 88 or not?Solution:Divisibility rule of 88 :
If number is divisible by 8 and 11, then number is also divisible by 88.
Divisibility rule of 8 :
The last three digit is divisible by 8, then number is also divisible by 8.
Last 3 digit of 30448 is 448, which is divisible by 8.
:. 30448 is divisible by 8.
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)
3044color{red}{8}=>3044 - color{red}{8} = 3036303color{red}{6}=>303 - color{red}{6} = 29729color{red}{7}=>29 - color{red}{7} = 22Here 22 is divisible by 11.
:. 30448 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 :
3+4+8=15Sum of digits in even positions :
0+4=4Difference
=4-15=-11which is divisible by 11.
:. 30448 is divisible by 11.
30448 is divisible by 8 and 11.
:. 30448 is divisible by 88.
3. Check whether 30888 is divisible by 88 or not?Solution:Divisibility rule of 88 :
If number is divisible by 8 and 11, then number is also divisible by 88.
Divisibility rule of 8 :
The last three digit is divisible by 8, then number is also divisible by 8.
Last 3 digit of 30888 is 888, which is divisible by 8.
:. 30888 is divisible by 8.
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)
3088color{red}{8}=>3088 - color{red}{8} = 3080308color{red}{0}=>308 - color{red}{0} = 30830color{red}{8}=>30 - color{red}{8} = 22Here 22 is divisible by 11.
:. 30888 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 :
3+8+8=19Sum of digits in even positions :
0+8=8Difference
=8-19=-11which is divisible by 11.
:. 30888 is divisible by 11.
30888 is divisible by 8 and 11.
:. 30888 is divisible by 88.
4. Check whether 22027 is divisible by 88 or not?Solution:Divisibility rule of 88 :
If number is divisible by 8 and 11, then number is also divisible by 88.
Divisibility rule of 8 :
The last three digit is divisible by 8, then number is also divisible by 8.
Last 3 digit of 22027 is 27, which is not divisible by 8.
:. 22027 is not divisible by 8.
Hence 22027 is also not divisible by 88.
5. Check whether 29356 is divisible by 88 or not?Solution:Divisibility rule of 88 :
If number is divisible by 8 and 11, then number is also divisible by 88.
Divisibility rule of 8 :
The last three digit is divisible by 8, then number is also divisible by 8.
Last 3 digit of 29356 is 356, which is not divisible by 8.
:. 29356 is not divisible by 8.
Hence 29356 is also not divisible by 88.
6. Check whether 34945 is divisible by 88 or not?Solution:Divisibility rule of 88 :
If number is divisible by 8 and 11, then number is also divisible by 88.
Divisibility rule of 8 :
The last three digit is divisible by 8, then number is also divisible by 8.
Last 3 digit of 34945 is 945, which is not divisible by 8.
:. 34945 is not divisible by 8.
Hence 34945 is also not divisible by 88.
This material is intended as a summary. Use your textbook for detail explanation.
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