1. Check whether 23925 is divisible by 87 or not?Solution:Divisibility rule of 87 :
26 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 87, then number is also divisible by 87.
(Apply this rule to the answer again if necessary)
`2392color{red}{5}=>2392 - color{red}{5} xx 26 = 2392 -130 = 2262`
`226color{red}{2}=>226 - color{red}{2} xx 26 = 226 -52 = 174`
`17color{red}{4}=>17 - color{red}{4} xx 26 = 17 -104 = -87`
Here -87 is divisible by 87.
`:.` 23925 is divisible by 87.
Method-2 : Divisibility rule of 87 :
If number is divisible by 3 and 29, then number is also divisible by 87.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 23925 is `2+3+9+2+5=21`, which is divisible by 3.
`:.` 23925 is divisible by 3.
Divisibility rule of 29 :
3 times the last digit and add it to the rest of the number.
If the answer is divisible by 29, then number is also divisible by 29.
(Apply this rule to the answer again if necessary)
`2392color{red}{5}=>2392 + color{red}{5} xx 3 = 2392 +15 = 2407`
`240color{red}{7}=>240 + color{red}{7} xx 3 = 240 +21 = 261`
`26color{red}{1}=>26 + color{red}{1} xx 3 = 26 +3 = 29`
Here 29 is divisible by 29.
`:.` 23925 is divisible by 29.
23925 is divisible by 3 and 29.
`:.` 23925 is divisible by 87.
2. Check whether 29667 is divisible by 87 or not?Solution:Divisibility rule of 87 :
26 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 87, then number is also divisible by 87.
(Apply this rule to the answer again if necessary)
`2966color{red}{7}=>2966 - color{red}{7} xx 26 = 2966 -182 = 2784`
`278color{red}{4}=>278 - color{red}{4} xx 26 = 278 -104 = 174`
`17color{red}{4}=>17 - color{red}{4} xx 26 = 17 -104 = -87`
Here -87 is divisible by 87.
`:.` 29667 is divisible by 87.
Method-2 : Divisibility rule of 87 :
If number is divisible by 3 and 29, then number is also divisible by 87.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 29667 is `2+9+6+6+7=30`, which is divisible by 3.
`:.` 29667 is divisible by 3.
Divisibility rule of 29 :
3 times the last digit and add it to the rest of the number.
If the answer is divisible by 29, then number is also divisible by 29.
(Apply this rule to the answer again if necessary)
`2966color{red}{7}=>2966 + color{red}{7} xx 3 = 2966 +21 = 2987`
`298color{red}{7}=>298 + color{red}{7} xx 3 = 298 +21 = 319`
`31color{red}{9}=>31 + color{red}{9} xx 3 = 31 +27 = 58`
Here 58 is divisible by 29.
`:.` 29667 is divisible by 29.
29667 is divisible by 3 and 29.
`:.` 29667 is divisible by 87.
3. Check whether 32451 is divisible by 87 or not?Solution:Divisibility rule of 87 :
26 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 87, then number is also divisible by 87.
(Apply this rule to the answer again if necessary)
`3245color{red}{1}=>3245 - color{red}{1} xx 26 = 3245 -26 = 3219`
`321color{red}{9}=>321 - color{red}{9} xx 26 = 321 -234 = 87`
Here 87 is divisible by 87.
`:.` 32451 is divisible by 87.
Method-2 : Divisibility rule of 87 :
If number is divisible by 3 and 29, then number is also divisible by 87.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 32451 is `3+2+4+5+1=15`, which is divisible by 3.
`:.` 32451 is divisible by 3.
Divisibility rule of 29 :
3 times the last digit and add it to the rest of the number.
If the answer is divisible by 29, then number is also divisible by 29.
(Apply this rule to the answer again if necessary)
`3245color{red}{1}=>3245 + color{red}{1} xx 3 = 3245 +3 = 3248`
`324color{red}{8}=>324 + color{red}{8} xx 3 = 324 +24 = 348`
`34color{red}{8}=>34 + color{red}{8} xx 3 = 34 +24 = 58`
Here 58 is divisible by 29.
`:.` 32451 is divisible by 29.
32451 is divisible by 3 and 29.
`:.` 32451 is divisible by 87.
4. Check whether 24240 is divisible by 87 or not?Solution:Divisibility rule of 87 :
26 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 87, then number is also divisible by 87.
(Apply this rule to the answer again if necessary)
`2424color{red}{0}=>2424 - color{red}{0} xx 26 = 2424 = 2424`
`242color{red}{4}=>242 - color{red}{4} xx 26 = 242 -104 = 138`
`13color{red}{8}=>13 - color{red}{8} xx 26 = 13 -208 = -195`
Here -195 is not divisible by 87.
`:.` 24240 is not divisible by 87.
Method-2 : Divisibility rule of 87 :
If number is divisible by 3 and 29, then number is also divisible by 87.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 24240 is `2+4+2+4+0=12`, which is divisible by 3.
`:.` 24240 is divisible by 3.
Divisibility rule of 29 :
3 times the last digit and add it to the rest of the number.
If the answer is divisible by 29, then number is also divisible by 29.
(Apply this rule to the answer again if necessary)
`2424color{red}{0}=>2424 + color{red}{0} xx 3 = 2424 = 2424`
`242color{red}{4}=>242 + color{red}{4} xx 3 = 242 +12 = 254`
`25color{red}{4}=>25 + color{red}{4} xx 3 = 25 +12 = 37`
Here 37 is not divisible by 29.
`:.` 24240 is not divisible by 29.
Hence 24240 is also not divisible by 87.
5. Check whether 27842 is divisible by 87 or not?Solution:Divisibility rule of 87 :
26 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 87, then number is also divisible by 87.
(Apply this rule to the answer again if necessary)
`2784color{red}{2}=>2784 - color{red}{2} xx 26 = 2784 -52 = 2732`
`273color{red}{2}=>273 - color{red}{2} xx 26 = 273 -52 = 221`
`22color{red}{1}=>22 - color{red}{1} xx 26 = 22 -26 = -4`
Here -4 is not divisible by 87.
`:.` 27842 is not divisible by 87.
Method-2 : Divisibility rule of 87 :
If number is divisible by 3 and 29, then number is also divisible by 87.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 27842 is `2+7+8+4+2=23`, which is not divisible by 3.
`:.` 27842 is not divisible by 3.
Hence 27842 is also not divisible by 87.
6. Check whether 33492 is divisible by 87 or not?Solution:Divisibility rule of 87 :
26 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 87, then number is also divisible by 87.
(Apply this rule to the answer again if necessary)
`3349color{red}{2}=>3349 - color{red}{2} xx 26 = 3349 -52 = 3297`
`329color{red}{7}=>329 - color{red}{7} xx 26 = 329 -182 = 147`
`14color{red}{7}=>14 - color{red}{7} xx 26 = 14 -182 = -168`
Here -168 is not divisible by 87.
`:.` 33492 is not divisible by 87.
Method-2 : Divisibility rule of 87 :
If number is divisible by 3 and 29, then number is also divisible by 87.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 33492 is `3+3+4+9+2=21`, which is divisible by 3.
`:.` 33492 is divisible by 3.
Divisibility rule of 29 :
3 times the last digit and add it to the rest of the number.
If the answer is divisible by 29, then number is also divisible by 29.
(Apply this rule to the answer again if necessary)
`3349color{red}{2}=>3349 + color{red}{2} xx 3 = 3349 +6 = 3355`
`335color{red}{5}=>335 + color{red}{5} xx 3 = 335 +15 = 350`
`35color{red}{0}=>35 + color{red}{0} xx 3 = 35 = 35`
Here 35 is not divisible by 29.
`:.` 33492 is not divisible by 29.
Hence 33492 is also not divisible by 87.
This material is intended as a summary. Use your textbook for detail explanation.
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