1. Check whether 6138 is divisible by 22 or not?Solution:Divisibility rule of 22 :
If number is divisible by 2 and 11, then number is also divisible by 22.
Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.
Last digit of 6138 is 8, which is divisible by 2.
`:.` 6138 is divisible by 2.
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)
`613color{red}{8}=>613 - color{red}{8} = 605`
`60color{red}{5}=>60 - color{red}{5} = 55`
Here 55 is divisible by 11.
`:.` 6138 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=9`
Sum of digits in even positions : `6+3=9`
Difference `=9-9=0`
which is divisible by 11.
`:.` 6138 is divisible by 11.
6138 is divisible by 2 and 11.
`:.` 6138 is divisible by 22.
2. Check whether 7436 is divisible by 22 or not?Solution:Divisibility rule of 22 :
If number is divisible by 2 and 11, then number is also divisible by 22.
Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.
Last digit of 7436 is 6, which is divisible by 2.
`:.` 7436 is divisible by 2.
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)
`743color{red}{6}=>743 - color{red}{6} = 737`
`73color{red}{7}=>73 - color{red}{7} = 66`
Here 66 is divisible by 11.
`:.` 7436 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 : `4+6=10`
Sum of digits in even positions : `7+3=10`
Difference `=10-10=0`
which is divisible by 11.
`:.` 7436 is divisible by 11.
7436 is divisible by 2 and 11.
`:.` 7436 is divisible by 22.
3. Check whether 8712 is divisible by 22 or not?Solution:Divisibility rule of 22 :
If number is divisible by 2 and 11, then number is also divisible by 22.
Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.
Last digit of 8712 is 2, which is divisible by 2.
`:.` 8712 is divisible by 2.
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)
`871color{red}{2}=>871 - color{red}{2} = 869`
`86color{red}{9}=>86 - color{red}{9} = 77`
Here 77 is divisible by 11.
`:.` 8712 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 : `7+2=9`
Sum of digits in even positions : `8+1=9`
Difference `=9-9=0`
which is divisible by 11.
`:.` 8712 is divisible by 11.
8712 is divisible by 2 and 11.
`:.` 8712 is divisible by 22.
4. Check whether 6383 is divisible by 22 or not?Solution:Divisibility rule of 22 :
If number is divisible by 2 and 11, then number is also divisible by 22.
Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.
Last digit of 6383 is 3, which is not divisible by 2.
`:.` 6383 is not divisible by 2.
Hence 6383 is also not divisible by 22.
5. Check whether 7426 is divisible by 22 or not?Solution:Divisibility rule of 22 :
If number is divisible by 2 and 11, then number is also divisible by 22.
Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.
Last digit of 7426 is 6, which is divisible by 2.
`:.` 7426 is divisible by 2.
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)
`742color{red}{6}=>742 - color{red}{6} = 736`
`73color{red}{6}=>73 - color{red}{6} = 67`
Here 67 is not divisible by 11.
`:.` 7426 is not 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 : `4+6=10`
Sum of digits in even positions : `7+2=9`
Difference `=9-10=-1`
which is not divisible by 11.
`:.` 7426 is not divisible by 11.
Hence 7426 is also not divisible by 22.
6. Check whether 8432 is divisible by 22 or not?Solution:Divisibility rule of 22 :
If number is divisible by 2 and 11, then number is also divisible by 22.
Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.
Last digit of 8432 is 2, which is divisible by 2.
`:.` 8432 is divisible by 2.
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)
`843color{red}{2}=>843 - color{red}{2} = 841`
`84color{red}{1}=>84 - color{red}{1} = 83`
Here 83 is not divisible by 11.
`:.` 8432 is not 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 : `4+2=6`
Sum of digits in even positions : `8+3=11`
Difference `=11-6=5`
which is not divisible by 11.
`:.` 8432 is not divisible by 11.
Hence 8432 is also not divisible by 22.
This material is intended as a summary. Use your textbook for detail explanation.
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