1. Check whether 18711 is divisible by 63 or not?Solution:Divisibility rule of 63 :
19 times the last digit and add it to the rest of the number.
If the answer is divisible by 63, then number is also divisible by 63.
(Apply this rule to the answer again if necessary)
`1871color{red}{1}=>1871 + color{red}{1} xx 19 = 1871 +19 = 1890`
`189color{red}{0}=>189 + color{red}{0} xx 19 = 189 = 189`
`18color{red}{9}=>18 + color{red}{9} xx 19 = 18 +171 = 189`
Here 189 is divisible by 63.
`:.` 18711 is divisible by 63.
Method-2 : Divisibility rule of 63 :
If number is divisible by 9 and 7, then number is also divisible by 63.
Divisibility rule of 9 :
The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 18711 is `1+8+7+1+1=18`, which is divisible by 9.
`:.` 18711 is divisible by 9.
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)
`1871color{red}{1}=>1871 - color{red}{1} xx 2 = 1871 -2 = 1869`
`186color{red}{9}=>186 - color{red}{9} xx 2 = 186 -18 = 168`
`16color{red}{8}=>16 - color{red}{8} xx 2 = 16 -16 = 0`
Here 0 is divisible by 7.
`:.` 18711 is divisible by 7.
18711 is divisible by 9 and 7.
`:.` 18711 is divisible by 63.
2. Check whether 19026 is divisible by 63 or not?Solution:Divisibility rule of 63 :
19 times the last digit and add it to the rest of the number.
If the answer is divisible by 63, then number is also divisible by 63.
(Apply this rule to the answer again if necessary)
`1902color{red}{6}=>1902 + color{red}{6} xx 19 = 1902 +114 = 2016`
`201color{red}{6}=>201 + color{red}{6} xx 19 = 201 +114 = 315`
`31color{red}{5}=>31 + color{red}{5} xx 19 = 31 +95 = 126`
`12color{red}{6}=>12 + color{red}{6} xx 19 = 12 +114 = 126`
Here 126 is divisible by 63.
`:.` 19026 is divisible by 63.
Method-2 : Divisibility rule of 63 :
If number is divisible by 9 and 7, then number is also divisible by 63.
Divisibility rule of 9 :
The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 19026 is `1+9+0+2+6=18`, which is divisible by 9.
`:.` 19026 is divisible by 9.
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)
`1902color{red}{6}=>1902 - color{red}{6} xx 2 = 1902 -12 = 1890`
`189color{red}{0}=>189 - color{red}{0} xx 2 = 189 = 189`
`18color{red}{9}=>18 - color{red}{9} xx 2 = 18 -18 = 0`
Here 0 is divisible by 7.
`:.` 19026 is divisible by 7.
19026 is divisible by 9 and 7.
`:.` 19026 is divisible by 63.
3. Check whether 24570 is divisible by 63 or not?Solution:Divisibility rule of 63 :
19 times the last digit and add it to the rest of the number.
If the answer is divisible by 63, then number is also divisible by 63.
(Apply this rule to the answer again if necessary)
`2457color{red}{0}=>2457 + color{red}{0} xx 19 = 2457 = 2457`
`245color{red}{7}=>245 + color{red}{7} xx 19 = 245 +133 = 378`
`37color{red}{8}=>37 + color{red}{8} xx 19 = 37 +152 = 189`
`18color{red}{9}=>18 + color{red}{9} xx 19 = 18 +171 = 189`
Here 189 is divisible by 63.
`:.` 24570 is divisible by 63.
Method-2 : Divisibility rule of 63 :
If number is divisible by 9 and 7, then number is also divisible by 63.
Divisibility rule of 9 :
The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 24570 is `2+4+5+7+0=18`, which is divisible by 9.
`:.` 24570 is divisible by 9.
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)
`2457color{red}{0}=>2457 - color{red}{0} xx 2 = 2457 = 2457`
`245color{red}{7}=>245 - color{red}{7} xx 2 = 245 -14 = 231`
`23color{red}{1}=>23 - color{red}{1} xx 2 = 23 -2 = 21`
Here 21 is divisible by 7.
`:.` 24570 is divisible by 7.
24570 is divisible by 9 and 7.
`:.` 24570 is divisible by 63.
4. Check whether 18569 is divisible by 63 or not?Solution:Divisibility rule of 63 :
19 times the last digit and add it to the rest of the number.
If the answer is divisible by 63, then number is also divisible by 63.
(Apply this rule to the answer again if necessary)
`1856color{red}{9}=>1856 + color{red}{9} xx 19 = 1856 +171 = 2027`
`202color{red}{7}=>202 + color{red}{7} xx 19 = 202 +133 = 335`
`33color{red}{5}=>33 + color{red}{5} xx 19 = 33 +95 = 128`
`12color{red}{8}=>12 + color{red}{8} xx 19 = 12 +152 = 164`
Here 164 is not divisible by 63.
`:.` 18569 is not divisible by 63.
Method-2 : Divisibility rule of 63 :
If number is divisible by 9 and 7, then number is also divisible by 63.
Divisibility rule of 9 :
The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 18569 is `1+8+5+6+9=29`, which is not divisible by 9.
`:.` 18569 is not divisible by 9.
Hence 18569 is also not divisible by 63.
5. Check whether 19600 is divisible by 63 or not?Solution:Divisibility rule of 63 :
19 times the last digit and add it to the rest of the number.
If the answer is divisible by 63, then number is also divisible by 63.
(Apply this rule to the answer again if necessary)
`1960color{red}{0}=>1960 + color{red}{0} xx 19 = 1960 = 1960`
`196color{red}{0}=>196 + color{red}{0} xx 19 = 196 = 196`
`19color{red}{6}=>19 + color{red}{6} xx 19 = 19 +114 = 133`
`13color{red}{3}=>13 + color{red}{3} xx 19 = 13 +57 = 70`
Here 70 is not divisible by 63.
`:.` 19600 is not divisible by 63.
Method-2 : Divisibility rule of 63 :
If number is divisible by 9 and 7, then number is also divisible by 63.
Divisibility rule of 9 :
The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 19600 is `1+9+6+0+0=16`, which is not divisible by 9.
`:.` 19600 is not divisible by 9.
Hence 19600 is also not divisible by 63.
6. Check whether 22545 is divisible by 63 or not?Solution:Divisibility rule of 63 :
19 times the last digit and add it to the rest of the number.
If the answer is divisible by 63, then number is also divisible by 63.
(Apply this rule to the answer again if necessary)
`2254color{red}{5}=>2254 + color{red}{5} xx 19 = 2254 +95 = 2349`
`234color{red}{9}=>234 + color{red}{9} xx 19 = 234 +171 = 405`
`40color{red}{5}=>40 + color{red}{5} xx 19 = 40 +95 = 135`
`13color{red}{5}=>13 + color{red}{5} xx 19 = 13 +95 = 108`
`10color{red}{8}=>10 + color{red}{8} xx 19 = 10 +152 = 162`
Here 162 is not divisible by 63.
`:.` 22545 is not divisible by 63.
Method-2 : Divisibility rule of 63 :
If number is divisible by 9 and 7, then number is also divisible by 63.
Divisibility rule of 9 :
The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 22545 is `2+2+5+4+5=18`, which is divisible by 9.
`:.` 22545 is divisible by 9.
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)
`2254color{red}{5}=>2254 - color{red}{5} xx 2 = 2254 -10 = 2244`
`224color{red}{4}=>224 - color{red}{4} xx 2 = 224 -8 = 216`
`21color{red}{6}=>21 - color{red}{6} xx 2 = 21 -12 = 9`
Here 9 is not divisible by 7.
`:.` 22545 is not divisible by 7.
Hence 22545 is also not divisible by 63.
This material is intended as a summary. Use your textbook for detail explanation.
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