1. Check whether 28413 is divisible by 99 or not?Solution:Divisibility rule of 99 :
10 times the last digit and add it to the rest of the number.
If the answer is divisible by 99, then number is also divisible by 99.
(Apply this rule to the answer again if necessary)
`2841color{red}{3}=>2841 + color{red}{3} xx 10 = 2841 +30 = 2871`
`287color{red}{1}=>287 + color{red}{1} xx 10 = 287 +10 = 297`
`29color{red}{7}=>29 + color{red}{7} xx 10 = 29 +70 = 99`
Here 99 is divisible by 99.
`:.` 28413 is divisible by 99.
Method-2 : Divisibility rule of 99 :
If number is divisible by 9 and 11, then number is also divisible by 99.
Divisibility rule of 9 :
The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 28413 is `2+8+4+1+3=18`, which is divisible by 9.
`:.` 28413 is divisible by 9.
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)
`2841color{red}{3}=>2841 - color{red}{3} = 2838`
`283color{red}{8}=>283 - color{red}{8} = 275`
`27color{red}{5}=>27 - color{red}{5} = 22`
Here 22 is divisible by 11.
`:.` 28413 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+4+3=9`
Sum of digits in even positions : `8+1=9`
Difference `=9-9=0`
which is divisible by 11.
`:.` 28413 is divisible by 11.
28413 is divisible by 9 and 11.
`:.` 28413 is divisible by 99.
2. Check whether 34155 is divisible by 99 or not?Solution:Divisibility rule of 99 :
10 times the last digit and add it to the rest of the number.
If the answer is divisible by 99, then number is also divisible by 99.
(Apply this rule to the answer again if necessary)
`3415color{red}{5}=>3415 + color{red}{5} xx 10 = 3415 +50 = 3465`
`346color{red}{5}=>346 + color{red}{5} xx 10 = 346 +50 = 396`
`39color{red}{6}=>39 + color{red}{6} xx 10 = 39 +60 = 99`
Here 99 is divisible by 99.
`:.` 34155 is divisible by 99.
Method-2 : Divisibility rule of 99 :
If number is divisible by 9 and 11, then number is also divisible by 99.
Divisibility rule of 9 :
The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 34155 is `3+4+1+5+5=18`, which is divisible by 9.
`:.` 34155 is divisible by 9.
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)
`3415color{red}{5}=>3415 - color{red}{5} = 3410`
`341color{red}{0}=>341 - color{red}{0} = 341`
`34color{red}{1}=>34 - color{red}{1} = 33`
Here 33 is divisible by 11.
`:.` 34155 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+1+5=9`
Sum of digits in even positions : `4+5=9`
Difference `=9-9=0`
which is divisible by 11.
`:.` 34155 is divisible by 11.
34155 is divisible by 9 and 11.
`:.` 34155 is divisible by 99.
3. Check whether 34947 is divisible by 99 or not?Solution:Divisibility rule of 99 :
10 times the last digit and add it to the rest of the number.
If the answer is divisible by 99, then number is also divisible by 99.
(Apply this rule to the answer again if necessary)
`3494color{red}{7}=>3494 + color{red}{7} xx 10 = 3494 +70 = 3564`
`356color{red}{4}=>356 + color{red}{4} xx 10 = 356 +40 = 396`
`39color{red}{6}=>39 + color{red}{6} xx 10 = 39 +60 = 99`
Here 99 is divisible by 99.
`:.` 34947 is divisible by 99.
Method-2 : Divisibility rule of 99 :
If number is divisible by 9 and 11, then number is also divisible by 99.
Divisibility rule of 9 :
The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 34947 is `3+4+9+4+7=27`, which is divisible by 9.
`:.` 34947 is divisible by 9.
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)
`3494color{red}{7}=>3494 - color{red}{7} = 3487`
`348color{red}{7}=>348 - color{red}{7} = 341`
`34color{red}{1}=>34 - color{red}{1} = 33`
Here 33 is divisible by 11.
`:.` 34947 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+9+7=19`
Sum of digits in even positions : `4+4=8`
Difference `=8-19=-11`
which is divisible by 11.
`:.` 34947 is divisible by 11.
34947 is divisible by 9 and 11.
`:.` 34947 is divisible by 99.
4. Check whether 25063 is divisible by 99 or not?Solution:Divisibility rule of 99 :
10 times the last digit and add it to the rest of the number.
If the answer is divisible by 99, then number is also divisible by 99.
(Apply this rule to the answer again if necessary)
`2506color{red}{3}=>2506 + color{red}{3} xx 10 = 2506 +30 = 2536`
`253color{red}{6}=>253 + color{red}{6} xx 10 = 253 +60 = 313`
`31color{red}{3}=>31 + color{red}{3} xx 10 = 31 +30 = 61`
Here 61 is not divisible by 99.
`:.` 25063 is not divisible by 99.
Method-2 : Divisibility rule of 99 :
If number is divisible by 9 and 11, then number is also divisible by 99.
Divisibility rule of 9 :
The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 25063 is `2+5+0+6+3=16`, which is not divisible by 9.
`:.` 25063 is not divisible by 9.
Hence 25063 is also not divisible by 99.
5. Check whether 33004 is divisible by 99 or not?Solution:Divisibility rule of 99 :
10 times the last digit and add it to the rest of the number.
If the answer is divisible by 99, then number is also divisible by 99.
(Apply this rule to the answer again if necessary)
`3300color{red}{4}=>3300 + color{red}{4} xx 10 = 3300 +40 = 3340`
`334color{red}{0}=>334 + color{red}{0} xx 10 = 334 = 334`
`33color{red}{4}=>33 + color{red}{4} xx 10 = 33 +40 = 73`
Here 73 is not divisible by 99.
`:.` 33004 is not divisible by 99.
Method-2 : Divisibility rule of 99 :
If number is divisible by 9 and 11, then number is also divisible by 99.
Divisibility rule of 9 :
The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 33004 is `3+3+0+0+4=10`, which is not divisible by 9.
`:.` 33004 is not divisible by 9.
Hence 33004 is also not divisible by 99.
6. Check whether 35129 is divisible by 99 or not?Solution:Divisibility rule of 99 :
10 times the last digit and add it to the rest of the number.
If the answer is divisible by 99, then number is also divisible by 99.
(Apply this rule to the answer again if necessary)
`3512color{red}{9}=>3512 + color{red}{9} xx 10 = 3512 +90 = 3602`
`360color{red}{2}=>360 + color{red}{2} xx 10 = 360 +20 = 380`
`38color{red}{0}=>38 + color{red}{0} xx 10 = 38 = 38`
Here 38 is not divisible by 99.
`:.` 35129 is not divisible by 99.
Method-2 : Divisibility rule of 99 :
If number is divisible by 9 and 11, then number is also divisible by 99.
Divisibility rule of 9 :
The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 35129 is `3+5+1+2+9=20`, which is not divisible by 9.
`:.` 35129 is not divisible by 9.
Hence 35129 is also not divisible by 99.
This material is intended as a summary. Use your textbook for detail explanation.
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