1. Check whether 22946 is divisible by 77 or not?Solution:Divisibility rule of 77 :
23 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 77, then number is also divisible by 77.
(Apply this rule to the answer again if necessary)
`2294color{red}{6}=>2294 - color{red}{6} xx 23 = 2294 -138 = 2156`
`215color{red}{6}=>215 - color{red}{6} xx 23 = 215 -138 = 77`
Here 77 is divisible by 77.
`:.` 22946 is divisible by 77.
Method-2 : Divisibility rule of 77 :
If number is divisible by 7 and 11, then number is also divisible by 77.
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)
`2294color{red}{6}=>2294 - color{red}{6} xx 2 = 2294 -12 = 2282`
`228color{red}{2}=>228 - color{red}{2} xx 2 = 228 -4 = 224`
`22color{red}{4}=>22 - color{red}{4} xx 2 = 22 -8 = 14`
Here 14 is divisible by 7.
`:.` 22946 is divisible by 7.
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)
`2294color{red}{6}=>2294 - color{red}{6} = 2288`
`228color{red}{8}=>228 - color{red}{8} = 220`
`22color{red}{0}=>22 - color{red}{0} = 22`
Here 22 is divisible by 11.
`:.` 22946 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+9+6=17`
Sum of digits in even positions : `2+4=6`
Difference `=6-17=-11`
which is divisible by 11.
`:.` 22946 is divisible by 11.
22946 is divisible by 7 and 11.
`:.` 22946 is divisible by 77.
2. Check whether 26488 is divisible by 77 or not?Solution:Divisibility rule of 77 :
23 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 77, then number is also divisible by 77.
(Apply this rule to the answer again if necessary)
`2648color{red}{8}=>2648 - color{red}{8} xx 23 = 2648 -184 = 2464`
`246color{red}{4}=>246 - color{red}{4} xx 23 = 246 -92 = 154`
`15color{red}{4}=>15 - color{red}{4} xx 23 = 15 -92 = -77`
Here -77 is divisible by 77.
`:.` 26488 is divisible by 77.
Method-2 : Divisibility rule of 77 :
If number is divisible by 7 and 11, then number is also divisible by 77.
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)
`2648color{red}{8}=>2648 - color{red}{8} xx 2 = 2648 -16 = 2632`
`263color{red}{2}=>263 - color{red}{2} xx 2 = 263 -4 = 259`
`25color{red}{9}=>25 - color{red}{9} xx 2 = 25 -18 = 7`
Here 7 is divisible by 7.
`:.` 26488 is divisible by 7.
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)
`2648color{red}{8}=>2648 - color{red}{8} = 2640`
`264color{red}{0}=>264 - color{red}{0} = 264`
`26color{red}{4}=>26 - color{red}{4} = 22`
Here 22 is divisible by 11.
`:.` 26488 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+8=14`
Sum of digits in even positions : `6+8=14`
Difference `=14-14=0`
which is divisible by 11.
`:.` 26488 is divisible by 11.
26488 is divisible by 7 and 11.
`:.` 26488 is divisible by 77.
3. Check whether 29337 is divisible by 77 or not?Solution:Divisibility rule of 77 :
23 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 77, then number is also divisible by 77.
(Apply this rule to the answer again if necessary)
`2933color{red}{7}=>2933 - color{red}{7} xx 23 = 2933 -161 = 2772`
`277color{red}{2}=>277 - color{red}{2} xx 23 = 277 -46 = 231`
`23color{red}{1}=>23 - color{red}{1} xx 23 = 23 -23 = 0`
Here 0 is divisible by 77.
`:.` 29337 is divisible by 77.
Method-2 : Divisibility rule of 77 :
If number is divisible by 7 and 11, then number is also divisible by 77.
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)
`2933color{red}{7}=>2933 - color{red}{7} xx 2 = 2933 -14 = 2919`
`291color{red}{9}=>291 - color{red}{9} xx 2 = 291 -18 = 273`
`27color{red}{3}=>27 - color{red}{3} xx 2 = 27 -6 = 21`
Here 21 is divisible by 7.
`:.` 29337 is divisible by 7.
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)
`2933color{red}{7}=>2933 - color{red}{7} = 2926`
`292color{red}{6}=>292 - color{red}{6} = 286`
`28color{red}{6}=>28 - color{red}{6} = 22`
Here 22 is divisible by 11.
`:.` 29337 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+3+7=12`
Sum of digits in even positions : `9+3=12`
Difference `=12-12=0`
which is divisible by 11.
`:.` 29337 is divisible by 11.
29337 is divisible by 7 and 11.
`:.` 29337 is divisible by 77.
4. Check whether 19270 is divisible by 77 or not?Solution:Divisibility rule of 77 :
23 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 77, then number is also divisible by 77.
(Apply this rule to the answer again if necessary)
`1927color{red}{0}=>1927 - color{red}{0} xx 23 = 1927 = 1927`
`192color{red}{7}=>192 - color{red}{7} xx 23 = 192 -161 = 31`
Here 31 is not divisible by 77.
`:.` 19270 is not divisible by 77.
Method-2 : Divisibility rule of 77 :
If number is divisible by 7 and 11, then number is also divisible by 77.
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)
`1927color{red}{0}=>1927 - color{red}{0} xx 2 = 1927 = 1927`
`192color{red}{7}=>192 - color{red}{7} xx 2 = 192 -14 = 178`
`17color{red}{8}=>17 - color{red}{8} xx 2 = 17 -16 = 1`
Here 1 is not divisible by 7.
`:.` 19270 is not divisible by 7.
Hence 19270 is also not divisible by 77.
5. Check whether 24256 is divisible by 77 or not?Solution:Divisibility rule of 77 :
23 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 77, then number is also divisible by 77.
(Apply this rule to the answer again if necessary)
`2425color{red}{6}=>2425 - color{red}{6} xx 23 = 2425 -138 = 2287`
`228color{red}{7}=>228 - color{red}{7} xx 23 = 228 -161 = 67`
Here 67 is not divisible by 77.
`:.` 24256 is not divisible by 77.
Method-2 : Divisibility rule of 77 :
If number is divisible by 7 and 11, then number is also divisible by 77.
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)
`2425color{red}{6}=>2425 - color{red}{6} xx 2 = 2425 -12 = 2413`
`241color{red}{3}=>241 - color{red}{3} xx 2 = 241 -6 = 235`
`23color{red}{5}=>23 - color{red}{5} xx 2 = 23 -10 = 13`
Here 13 is not divisible by 7.
`:.` 24256 is not divisible by 7.
Hence 24256 is also not divisible by 77.
6. Check whether 27879 is divisible by 77 or not?Solution:Divisibility rule of 77 :
23 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 77, then number is also divisible by 77.
(Apply this rule to the answer again if necessary)
`2787color{red}{9}=>2787 - color{red}{9} xx 23 = 2787 -207 = 2580`
`258color{red}{0}=>258 - color{red}{0} xx 23 = 258 = 258`
`25color{red}{8}=>25 - color{red}{8} xx 23 = 25 -184 = -159`
Here -159 is not divisible by 77.
`:.` 27879 is not divisible by 77.
Method-2 : Divisibility rule of 77 :
If number is divisible by 7 and 11, then number is also divisible by 77.
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)
`2787color{red}{9}=>2787 - color{red}{9} xx 2 = 2787 -18 = 2769`
`276color{red}{9}=>276 - color{red}{9} xx 2 = 276 -18 = 258`
`25color{red}{8}=>25 - color{red}{8} xx 2 = 25 -16 = 9`
Here 9 is not divisible by 7.
`:.` 27879 is not divisible by 7.
Hence 27879 is also not divisible by 77.
This material is intended as a summary. Use your textbook for detail explanation.
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