1. Check whether 22680 is divisible by 84 or not?Solution:Divisibility rule of 84 :
If number is divisible by 4,3 and 7, then number is also divisible by 84.
Divisibility rule of 4 :
The last two digit is divisible by 4, then number is also divisible by 4.
Last 2 digit of 22680 is 80, which is divisible by 4.
:. 22680 is divisible by 4.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 22680 is
2+2+6+8+0=18, which is divisible by 3.
:. 22680 is divisible by 3.
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)
2268color{red}{0}=>2268 - color{red}{0} xx 2 = 2268 = 2268226color{red}{8}=>226 - color{red}{8} xx 2 = 226 -16 = 21021color{red}{0}=>21 - color{red}{0} xx 2 = 21 = 21Here 21 is divisible by 7.
:. 22680 is divisible by 7.
22680 is divisible by 4,3 and 7.
:. 22680 is divisible by 84.
2. Check whether 27804 is divisible by 84 or not?Solution:Divisibility rule of 84 :
If number is divisible by 4,3 and 7, then number is also divisible by 84.
Divisibility rule of 4 :
The last two digit is divisible by 4, then number is also divisible by 4.
Last 2 digit of 27804 is 4, which is divisible by 4.
:. 27804 is divisible by 4.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 27804 is
2+7+8+0+4=21, which is divisible by 3.
:. 27804 is divisible by 3.
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)
2780color{red}{4}=>2780 - color{red}{4} xx 2 = 2780 -8 = 2772277color{red}{2}=>277 - color{red}{2} xx 2 = 277 -4 = 27327color{red}{3}=>27 - color{red}{3} xx 2 = 27 -6 = 21Here 21 is divisible by 7.
:. 27804 is divisible by 7.
27804 is divisible by 4,3 and 7.
:. 27804 is divisible by 84.
3. Check whether 31080 is divisible by 84 or not?Solution:Divisibility rule of 84 :
If number is divisible by 4,3 and 7, then number is also divisible by 84.
Divisibility rule of 4 :
The last two digit is divisible by 4, then number is also divisible by 4.
Last 2 digit of 31080 is 80, which is divisible by 4.
:. 31080 is divisible by 4.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 31080 is
3+1+0+8+0=12, which is divisible by 3.
:. 31080 is divisible by 3.
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)
3108color{red}{0}=>3108 - color{red}{0} xx 2 = 3108 = 3108310color{red}{8}=>310 - color{red}{8} xx 2 = 310 -16 = 29429color{red}{4}=>29 - color{red}{4} xx 2 = 29 -8 = 21Here 21 is divisible by 7.
:. 31080 is divisible by 7.
31080 is divisible by 4,3 and 7.
:. 31080 is divisible by 84.
4. Check whether 24531 is divisible by 84 or not?Solution:Divisibility rule of 84 :
If number is divisible by 4,3 and 7, then number is also divisible by 84.
Divisibility rule of 4 :
The last two digit is divisible by 4, then number is also divisible by 4.
Last 2 digit of 24531 is 31, which is not divisible by 4.
:. 24531 is not divisible by 4.
Hence 24531 is also not divisible by 84.
5. Check whether 28869 is divisible by 84 or not?Solution:Divisibility rule of 84 :
If number is divisible by 4,3 and 7, then number is also divisible by 84.
Divisibility rule of 4 :
The last two digit is divisible by 4, then number is also divisible by 4.
Last 2 digit of 28869 is 69, which is not divisible by 4.
:. 28869 is not divisible by 4.
Hence 28869 is also not divisible by 84.
6. Check whether 30144 is divisible by 84 or not?Solution:Divisibility rule of 84 :
If number is divisible by 4,3 and 7, then number is also divisible by 84.
Divisibility rule of 4 :
The last two digit is divisible by 4, then number is also divisible by 4.
Last 2 digit of 30144 is 44, which is divisible by 4.
:. 30144 is divisible by 4.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 30144 is
3+0+1+4+4=12, which is divisible by 3.
:. 30144 is divisible by 3.
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)
3014color{red}{4}=>3014 - color{red}{4} xx 2 = 3014 -8 = 3006300color{red}{6}=>300 - color{red}{6} xx 2 = 300 -12 = 28828color{red}{8}=>28 - color{red}{8} xx 2 = 28 -16 = 12Here 12 is not divisible by 7.
:. 30144 is not divisible by 7.
Hence 30144 is also not divisible by 84.
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then