1. Check whether 24479 is divisible by 91 or not?Solution:Divisibility rule of 91 :
9 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 91, then number is also divisible by 91.
(Apply this rule to the answer again if necessary)
`2447color{red}{9}=>2447 - color{red}{9} xx 9 = 2447 -81 = 2366`
`236color{red}{6}=>236 - color{red}{6} xx 9 = 236 -54 = 182`
`18color{red}{2}=>18 - color{red}{2} xx 9 = 18 -18 = 0`
Here 0 is divisible by 91.
`:.` 24479 is divisible by 91.
Method-2 : Divisibility rule of 91 :
If number is divisible by 7 and 13, then number is also divisible by 91.
Divisibility rule of 7 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)
`2447color{red}{9}=>2447 - color{red}{9} xx 2 = 2447 -18 = 2429`
`242color{red}{9}=>242 - color{red}{9} xx 2 = 242 -18 = 224`
`22color{red}{4}=>22 - color{red}{4} xx 2 = 22 -8 = 14`
Here 14 is divisible by 7.
`:.` 24479 is divisible by 7.
Divisibility rule of 13 :
4 times the last digit and add it to the rest of the number.
If the answer is divisible by 13, then number is also divisible by 13.
(Apply this rule to the answer again if necessary)
`2447color{red}{9}=>2447 + color{red}{9} xx 4 = 2447 +36 = 2483`
`248color{red}{3}=>248 + color{red}{3} xx 4 = 248 +12 = 260`
`26color{red}{0}=>26 + color{red}{0} xx 4 = 26 = 26`
Here 26 is divisible by 13.
`:.` 24479 is divisible by 13.
24479 is divisible by 7 and 13.
`:.` 24479 is divisible by 91.
2. Check whether 31122 is divisible by 91 or not?Solution:Divisibility rule of 91 :
9 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 91, then number is also divisible by 91.
(Apply this rule to the answer again if necessary)
`3112color{red}{2}=>3112 - color{red}{2} xx 9 = 3112 -18 = 3094`
`309color{red}{4}=>309 - color{red}{4} xx 9 = 309 -36 = 273`
`27color{red}{3}=>27 - color{red}{3} xx 9 = 27 -27 = 0`
Here 0 is divisible by 91.
`:.` 31122 is divisible by 91.
Method-2 : Divisibility rule of 91 :
If number is divisible by 7 and 13, then number is also divisible by 91.
Divisibility rule of 7 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)
`3112color{red}{2}=>3112 - color{red}{2} xx 2 = 3112 -4 = 3108`
`310color{red}{8}=>310 - color{red}{8} xx 2 = 310 -16 = 294`
`29color{red}{4}=>29 - color{red}{4} xx 2 = 29 -8 = 21`
Here 21 is divisible by 7.
`:.` 31122 is divisible by 7.
Divisibility rule of 13 :
4 times the last digit and add it to the rest of the number.
If the answer is divisible by 13, then number is also divisible by 13.
(Apply this rule to the answer again if necessary)
`3112color{red}{2}=>3112 + color{red}{2} xx 4 = 3112 +8 = 3120`
`312color{red}{0}=>312 + color{red}{0} xx 4 = 312 = 312`
`31color{red}{2}=>31 + color{red}{2} xx 4 = 31 +8 = 39`
Here 39 is divisible by 13.
`:.` 31122 is divisible by 13.
31122 is divisible by 7 and 13.
`:.` 31122 is divisible by 91.
3. Check whether 32669 is divisible by 91 or not?Solution:Divisibility rule of 91 :
9 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 91, then number is also divisible by 91.
(Apply this rule to the answer again if necessary)
`3266color{red}{9}=>3266 - color{red}{9} xx 9 = 3266 -81 = 3185`
`318color{red}{5}=>318 - color{red}{5} xx 9 = 318 -45 = 273`
`27color{red}{3}=>27 - color{red}{3} xx 9 = 27 -27 = 0`
Here 0 is divisible by 91.
`:.` 32669 is divisible by 91.
Method-2 : Divisibility rule of 91 :
If number is divisible by 7 and 13, then number is also divisible by 91.
Divisibility rule of 7 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)
`3266color{red}{9}=>3266 - color{red}{9} xx 2 = 3266 -18 = 3248`
`324color{red}{8}=>324 - color{red}{8} xx 2 = 324 -16 = 308`
`30color{red}{8}=>30 - color{red}{8} xx 2 = 30 -16 = 14`
Here 14 is divisible by 7.
`:.` 32669 is divisible by 7.
Divisibility rule of 13 :
4 times the last digit and add it to the rest of the number.
If the answer is divisible by 13, then number is also divisible by 13.
(Apply this rule to the answer again if necessary)
`3266color{red}{9}=>3266 + color{red}{9} xx 4 = 3266 +36 = 3302`
`330color{red}{2}=>330 + color{red}{2} xx 4 = 330 +8 = 338`
`33color{red}{8}=>33 + color{red}{8} xx 4 = 33 +32 = 65`
Here 65 is divisible by 13.
`:.` 32669 is divisible by 13.
32669 is divisible by 7 and 13.
`:.` 32669 is divisible by 91.
4. Check whether 24014 is divisible by 91 or not?Solution:Divisibility rule of 91 :
9 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 91, then number is also divisible by 91.
(Apply this rule to the answer again if necessary)
`2401color{red}{4}=>2401 - color{red}{4} xx 9 = 2401 -36 = 2365`
`236color{red}{5}=>236 - color{red}{5} xx 9 = 236 -45 = 191`
`19color{red}{1}=>19 - color{red}{1} xx 9 = 19 -9 = 10`
Here 10 is not divisible by 91.
`:.` 24014 is not divisible by 91.
Method-2 : Divisibility rule of 91 :
If number is divisible by 7 and 13, then number is also divisible by 91.
Divisibility rule of 7 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)
`2401color{red}{4}=>2401 - color{red}{4} xx 2 = 2401 -8 = 2393`
`239color{red}{3}=>239 - color{red}{3} xx 2 = 239 -6 = 233`
`23color{red}{3}=>23 - color{red}{3} xx 2 = 23 -6 = 17`
Here 17 is not divisible by 7.
`:.` 24014 is not divisible by 7.
Hence 24014 is also not divisible by 91.
5. Check whether 27396 is divisible by 91 or not?Solution:Divisibility rule of 91 :
9 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 91, then number is also divisible by 91.
(Apply this rule to the answer again if necessary)
`2739color{red}{6}=>2739 - color{red}{6} xx 9 = 2739 -54 = 2685`
`268color{red}{5}=>268 - color{red}{5} xx 9 = 268 -45 = 223`
`22color{red}{3}=>22 - color{red}{3} xx 9 = 22 -27 = -5`
Here -5 is not divisible by 91.
`:.` 27396 is not divisible by 91.
Method-2 : Divisibility rule of 91 :
If number is divisible by 7 and 13, then number is also divisible by 91.
Divisibility rule of 7 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)
`2739color{red}{6}=>2739 - color{red}{6} xx 2 = 2739 -12 = 2727`
`272color{red}{7}=>272 - color{red}{7} xx 2 = 272 -14 = 258`
`25color{red}{8}=>25 - color{red}{8} xx 2 = 25 -16 = 9`
Here 9 is not divisible by 7.
`:.` 27396 is not divisible by 7.
Hence 27396 is also not divisible by 91.
6. Check whether 36189 is divisible by 91 or not?Solution:Divisibility rule of 91 :
9 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 91, then number is also divisible by 91.
(Apply this rule to the answer again if necessary)
`3618color{red}{9}=>3618 - color{red}{9} xx 9 = 3618 -81 = 3537`
`353color{red}{7}=>353 - color{red}{7} xx 9 = 353 -63 = 290`
`29color{red}{0}=>29 - color{red}{0} xx 9 = 29 = 29`
Here 29 is not divisible by 91.
`:.` 36189 is not divisible by 91.
Method-2 : Divisibility rule of 91 :
If number is divisible by 7 and 13, then number is also divisible by 91.
Divisibility rule of 7 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)
`3618color{red}{9}=>3618 - color{red}{9} xx 2 = 3618 -18 = 3600`
`360color{red}{0}=>360 - color{red}{0} xx 2 = 360 = 360`
`36color{red}{0}=>36 - color{red}{0} xx 2 = 36 = 36`
Here 36 is not divisible by 7.
`:.` 36189 is not divisible by 7.
Hence 36189 is also not divisible by 91.
This material is intended as a summary. Use your textbook for detail explanation.
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