1. Check whether 15732 is divisible by 57 or not?Solution:Divisibility rule of 57 :
17 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 57, then number is also divisible by 57.
(Apply this rule to the answer again if necessary)
`1573color{red}{2}=>1573 - color{red}{2} xx 17 = 1573 -34 = 1539`
`153color{red}{9}=>153 - color{red}{9} xx 17 = 153 -153 = 0`
Here 0 is divisible by 57.
`:.` 15732 is divisible by 57.
Method-2 : Divisibility rule of 57 :
If number is divisible by 3 and 19, then number is also divisible by 57.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 15732 is `1+5+7+3+2=18`, which is divisible by 3.
`:.` 15732 is divisible by 3.
Divisibility rule of 19 :
2 times the last digit and add it to the rest of the number.
If the answer is divisible by 19, then number is also divisible by 19.
(Apply this rule to the answer again if necessary)
`1573color{red}{2}=>1573 + color{red}{2} xx 2 = 1573 +4 = 1577`
`157color{red}{7}=>157 + color{red}{7} xx 2 = 157 +14 = 171`
`17color{red}{1}=>17 + color{red}{1} xx 2 = 17 +2 = 19`
Here 19 is divisible by 19.
`:.` 15732 is divisible by 19.
15732 is divisible by 3 and 19.
`:.` 15732 is divisible by 57.
2. Check whether 18069 is divisible by 57 or not?Solution:Divisibility rule of 57 :
17 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 57, then number is also divisible by 57.
(Apply this rule to the answer again if necessary)
`1806color{red}{9}=>1806 - color{red}{9} xx 17 = 1806 -153 = 1653`
`165color{red}{3}=>165 - color{red}{3} xx 17 = 165 -51 = 114`
`11color{red}{4}=>11 - color{red}{4} xx 17 = 11 -68 = -57`
Here -57 is divisible by 57.
`:.` 18069 is divisible by 57.
Method-2 : Divisibility rule of 57 :
If number is divisible by 3 and 19, then number is also divisible by 57.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 18069 is `1+8+0+6+9=24`, which is divisible by 3.
`:.` 18069 is divisible by 3.
Divisibility rule of 19 :
2 times the last digit and add it to the rest of the number.
If the answer is divisible by 19, then number is also divisible by 19.
(Apply this rule to the answer again if necessary)
`1806color{red}{9}=>1806 + color{red}{9} xx 2 = 1806 +18 = 1824`
`182color{red}{4}=>182 + color{red}{4} xx 2 = 182 +8 = 190`
`19color{red}{0}=>19 + color{red}{0} xx 2 = 19 = 19`
Here 19 is divisible by 19.
`:.` 18069 is divisible by 19.
18069 is divisible by 3 and 19.
`:.` 18069 is divisible by 57.
3. Check whether 20634 is divisible by 57 or not?Solution:Divisibility rule of 57 :
17 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 57, then number is also divisible by 57.
(Apply this rule to the answer again if necessary)
`2063color{red}{4}=>2063 - color{red}{4} xx 17 = 2063 -68 = 1995`
`199color{red}{5}=>199 - color{red}{5} xx 17 = 199 -85 = 114`
`11color{red}{4}=>11 - color{red}{4} xx 17 = 11 -68 = -57`
Here -57 is divisible by 57.
`:.` 20634 is divisible by 57.
Method-2 : Divisibility rule of 57 :
If number is divisible by 3 and 19, then number is also divisible by 57.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 20634 is `2+0+6+3+4=15`, which is divisible by 3.
`:.` 20634 is divisible by 3.
Divisibility rule of 19 :
2 times the last digit and add it to the rest of the number.
If the answer is divisible by 19, then number is also divisible by 19.
(Apply this rule to the answer again if necessary)
`2063color{red}{4}=>2063 + color{red}{4} xx 2 = 2063 +8 = 2071`
`207color{red}{1}=>207 + color{red}{1} xx 2 = 207 +2 = 209`
`20color{red}{9}=>20 + color{red}{9} xx 2 = 20 +18 = 38`
Here 38 is divisible by 19.
`:.` 20634 is divisible by 19.
20634 is divisible by 3 and 19.
`:.` 20634 is divisible by 57.
4. Check whether 16428 is divisible by 57 or not?Solution:Divisibility rule of 57 :
17 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 57, then number is also divisible by 57.
(Apply this rule to the answer again if necessary)
`1642color{red}{8}=>1642 - color{red}{8} xx 17 = 1642 -136 = 1506`
`150color{red}{6}=>150 - color{red}{6} xx 17 = 150 -102 = 48`
Here 48 is not divisible by 57.
`:.` 16428 is not divisible by 57.
Method-2 : Divisibility rule of 57 :
If number is divisible by 3 and 19, then number is also divisible by 57.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 16428 is `1+6+4+2+8=21`, which is divisible by 3.
`:.` 16428 is divisible by 3.
Divisibility rule of 19 :
2 times the last digit and add it to the rest of the number.
If the answer is divisible by 19, then number is also divisible by 19.
(Apply this rule to the answer again if necessary)
`1642color{red}{8}=>1642 + color{red}{8} xx 2 = 1642 +16 = 1658`
`165color{red}{8}=>165 + color{red}{8} xx 2 = 165 +16 = 181`
`18color{red}{1}=>18 + color{red}{1} xx 2 = 18 +2 = 20`
Here 20 is not divisible by 19.
`:.` 16428 is not divisible by 19.
Hence 16428 is also not divisible by 57.
5. Check whether 19795 is divisible by 57 or not?Solution:Divisibility rule of 57 :
17 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 57, then number is also divisible by 57.
(Apply this rule to the answer again if necessary)
`1979color{red}{5}=>1979 - color{red}{5} xx 17 = 1979 -85 = 1894`
`189color{red}{4}=>189 - color{red}{4} xx 17 = 189 -68 = 121`
`12color{red}{1}=>12 - color{red}{1} xx 17 = 12 -17 = -5`
Here -5 is not divisible by 57.
`:.` 19795 is not divisible by 57.
Method-2 : Divisibility rule of 57 :
If number is divisible by 3 and 19, then number is also divisible by 57.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 19795 is `1+9+7+9+5=31`, which is not divisible by 3.
`:.` 19795 is not divisible by 3.
Hence 19795 is also not divisible by 57.
6. Check whether 21256 is divisible by 57 or not?Solution:Divisibility rule of 57 :
17 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 57, then number is also divisible by 57.
(Apply this rule to the answer again if necessary)
`2125color{red}{6}=>2125 - color{red}{6} xx 17 = 2125 -102 = 2023`
`202color{red}{3}=>202 - color{red}{3} xx 17 = 202 -51 = 151`
`15color{red}{1}=>15 - color{red}{1} xx 17 = 15 -17 = -2`
Here -2 is not divisible by 57.
`:.` 21256 is not divisible by 57.
Method-2 : Divisibility rule of 57 :
If number is divisible by 3 and 19, then number is also divisible by 57.
Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 21256 is `2+1+2+5+6=16`, which is not divisible by 3.
`:.` 21256 is not divisible by 3.
Hence 21256 is also not divisible by 57.
This material is intended as a summary. Use your textbook for detail explanation.
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