1. Check whether 23736 is divisible by 86 or not?Solution:Divisibility rule of 86 :
If number is divisible by 2 and 43, then number is also divisible by 86.
Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.
Last digit of 23736 is 6, which is divisible by 2.
`:.` 23736 is divisible by 2.
Divisibility rule of 43 :
13 times the last digit and add it to the rest of the number.
If the answer is divisible by 43, then number is also divisible by 43.
(Apply this rule to the answer again if necessary)
`2373color{red}{6}=>2373 + color{red}{6} xx 13 = 2373 +78 = 2451`
`245color{red}{1}=>245 + color{red}{1} xx 13 = 245 +13 = 258`
`25color{red}{8}=>25 + color{red}{8} xx 13 = 25 +104 = 129`
`12color{red}{9}=>12 + color{red}{9} xx 13 = 12 +117 = 129`
Here 129 is divisible by 43.
`:.` 23736 is divisible by 43.
23736 is divisible by 2 and 43.
`:.` 23736 is divisible by 86.
2. Check whether 27520 is divisible by 86 or not?Solution:Divisibility rule of 86 :
If number is divisible by 2 and 43, then number is also divisible by 86.
Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.
Last digit of 27520 is 0, which is divisible by 2.
`:.` 27520 is divisible by 2.
Divisibility rule of 43 :
13 times the last digit and add it to the rest of the number.
If the answer is divisible by 43, then number is also divisible by 43.
(Apply this rule to the answer again if necessary)
`2752color{red}{0}=>2752 + color{red}{0} xx 13 = 2752 = 2752`
`275color{red}{2}=>275 + color{red}{2} xx 13 = 275 +26 = 301`
`30color{red}{1}=>30 + color{red}{1} xx 13 = 30 +13 = 43`
Here 43 is divisible by 43.
`:.` 27520 is divisible by 43.
27520 is divisible by 2 and 43.
`:.` 27520 is divisible by 86.
3. Check whether 31132 is divisible by 86 or not?Solution:Divisibility rule of 86 :
If number is divisible by 2 and 43, then number is also divisible by 86.
Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.
Last digit of 31132 is 2, which is divisible by 2.
`:.` 31132 is divisible by 2.
Divisibility rule of 43 :
13 times the last digit and add it to the rest of the number.
If the answer is divisible by 43, then number is also divisible by 43.
(Apply this rule to the answer again if necessary)
`3113color{red}{2}=>3113 + color{red}{2} xx 13 = 3113 +26 = 3139`
`313color{red}{9}=>313 + color{red}{9} xx 13 = 313 +117 = 430`
`43color{red}{0}=>43 + color{red}{0} xx 13 = 43 = 43`
Here 43 is divisible by 43.
`:.` 31132 is divisible by 43.
31132 is divisible by 2 and 43.
`:.` 31132 is divisible by 86.
4. Check whether 22403 is divisible by 86 or not?Solution:Divisibility rule of 86 :
If number is divisible by 2 and 43, then number is also divisible by 86.
Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.
Last digit of 22403 is 3, which is not divisible by 2.
`:.` 22403 is not divisible by 2.
Hence 22403 is also not divisible by 86.
5. Check whether 26407 is divisible by 86 or not?Solution:Divisibility rule of 86 :
If number is divisible by 2 and 43, then number is also divisible by 86.
Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.
Last digit of 26407 is 7, which is not divisible by 2.
`:.` 26407 is not divisible by 2.
Hence 26407 is also not divisible by 86.
6. Check whether 32573 is divisible by 86 or not?Solution:Divisibility rule of 86 :
If number is divisible by 2 and 43, then number is also divisible by 86.
Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.
Last digit of 32573 is 3, which is not divisible by 2.
`:.` 32573 is not divisible by 2.
Hence 32573 is also not divisible by 86.
This material is intended as a summary. Use your textbook for detail explanation.
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