3. Examples (Divisibility test of 11 to 20)
1. Check whether 4213 is divisible by 11 or not?
Solution:
Division rule of 11 : Subtract the last digit from the rest of the number.
If the answer is divisible by 11, then number is also divisible by 11.
(Apply this rule to the answer again if necessary)
Check 4213 is divisible by 11 or not
`421color{red}{3}=>421 - color{red}{3} = 418`
`41color{red}{8}=>41 - color{red}{8} = 33`
Here 33 is divisible by 11.
`:.` 4213 is divisible by 11.
2. Check whether 4212 is divisible by 11 or not?
Solution:
Division rule of 11 : Subtract the last digit from the rest of the number.
If the answer is divisible by 11, then number is also divisible by 11.
(Apply this rule to the answer again if necessary)
Check 4212 is divisible by 11 or not
`421color{red}{2}=>421 - color{red}{2} = 419`
`41color{red}{9}=>41 - color{red}{9} = 32`
Here 32 is not divisible by 11.
`:.` 4212 is not divisible by 11.
3. Check whether 2712 is divisible by 12 or not?
Solution:
Division rule of 12 : If number is divisible by 4 and 3, then number is also divisible by 12.
Last 2 digit of 2712 is 12, which is divisible by 4.
`:.` 2712 is divisible by 4.
Sum of digits of 2712 is `2+7+1+2=12`, which is divisible by 3.
`:.` 2712 is divisible by 3.
2712 is divisible by 4 and 3.
`:.` 2712 is divisible by 12.
4. Check whether 2710 is divisible by 12 or not?
Solution:
Division rule of 12 : If number is divisible by 4 and 3, then number is also divisible by 12.
Last 2 digit of 2710 is 10, which is not divisible by 4.
`:.` 2710 is not divisible by 4.
Hence 2710 is also not divisible by 12.
5. Check whether 13273 is divisible by 13 or not?
Solution:
Division rule of 13 : 4 times the last digit and add it to the rest of the number.
If the answer is divisible by 13, then number is also divisible by 13.
(Apply this rule to the answer again if necessary)
Check 13273 is divisible by 13 or not
`1327color{red}{3}=>1327 + color{red}{3} xx 4 = 1327 +12 = 1339`
`133color{red}{9}=>133 + color{red}{9} xx 4 = 133 +36 = 169`
`16color{red}{9}=>16 + color{red}{9} xx 4 = 16 +36 = 52`
Here 52 is divisible by 13.
`:.` 13273 is divisible by 13.
6. Check whether 13272 is divisible by 13 or not?
Solution:
Division rule of 13 : 4 times the last digit and add it to the rest of the number.
If the answer is divisible by 13, then number is also divisible by 13.
(Apply this rule to the answer again if necessary)
Check 13272 is divisible by 13 or not
`1327color{red}{2}=>1327 + color{red}{2} xx 4 = 1327 +8 = 1335`
`133color{red}{5}=>133 + color{red}{5} xx 4 = 133 +20 = 153`
`15color{red}{3}=>15 + color{red}{3} xx 4 = 15 +12 = 27`
Here 27 is not divisible by 13.
`:.` 13272 is not divisible by 13.
7. Check whether 6706 is divisible by 14 or not?
Solution:
Division rule of 14 : If number is divisible by 2 and 7, then number is also divisible by 14.
Last digit of 6706 is 6, which is divisible by 2.
`:.` 6706 is divisible by 2.
Check 6706 is divisible by 7 or not
`670color{red}{6}=>670 - color{red}{6} xx 2 = 670 -12 = 658`
`65color{red}{8}=>65 - color{red}{8} xx 2 = 65 -16 = 49`
Here 49 is divisible by 7.
`:.` 6706 is divisible by 7.
6706 is divisible by 2 and 7.
`:.` 6706 is divisible by 14.
8. Check whether 6704 is divisible by 14 or not?
Solution:
Division rule of 14 : If number is divisible by 2 and 7, then number is also divisible by 14.
Last digit of 6704 is 4, which is divisible by 2.
`:.` 6704 is divisible by 2.
Check 6704 is divisible by 7 or not
`670color{red}{4}=>670 - color{red}{4} xx 2 = 670 -8 = 662`
`66color{red}{2}=>66 - color{red}{2} xx 2 = 66 -4 = 62`
Here 62 is not divisible by 7.
`:.` 6704 is not divisible by 7.
Hence 6704 is also not divisible by 14.
9. Check whether 3975 is divisible by 15 or not?
Solution:
Division rule of 15 : If number is divisible by 3 and 5, then number is also divisible by 15.
Sum of digits of 3975 is `3+9+7+5=24`, which is divisible by 3.
`:.` 3975 is divisible by 3.
Last digit of 3975 is 5.
`:.` 3975 is divisible by 5.
3975 is divisible by 3 and 5.
`:.` 3975 is divisible by 15.
10. Check whether 3970 is divisible by 15 or not?
Solution:
Division rule of 15 : If number is divisible by 3 and 5, then number is also divisible by 15.
Sum of digits of 3970 is `3+9+7+0=19`, which is not divisible by 3.
`:.` 3970 is not divisible by 3.
Hence 3970 is also not divisible by 15.
11. Check whether 10256 is divisible by 16 or not?
Solution:
Division rule of 16 : The last four digit is divisible by 16, then number is also divisible by 16.
Last 4 digit of 10256 is 256, which is divisible by 16.
`:.` 10256 is divisible by 16.
12. Check whether 10254 is divisible by 16 or not?
Solution:
Division rule of 16 : The last four digit is divisible by 16, then number is also divisible by 16.
Last 4 digit of 10254 is 254, which is not divisible by 16.
`:.` 10254 is not divisible by 16.
13. Check whether 17544 is divisible by 17 or not?
Solution:
Division rule of 17 : 5 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 17, then number is also divisible by 17.
(Apply this rule to the answer again if necessary)
Check 17544 is divisible by 17 or not
`1754color{red}{4}=>1754 - color{red}{4} xx 5 = 1754 -20 = 1734`
`173color{red}{4}=>173 - color{red}{4} xx 5 = 173 -20 = 153`
`15color{red}{3}=>15 - color{red}{3} xx 5 = 15 -15 = 0`
Here 0 is divisible by 17.
`:.` 17544 is divisible by 17.
14. Check whether 17543 is divisible by 17 or not?
Solution:
Division rule of 17 : 5 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 17, then number is also divisible by 17.
(Apply this rule to the answer again if necessary)
Check 17543 is divisible by 17 or not
`1754color{red}{3}=>1754 - color{red}{3} xx 5 = 1754 -15 = 1739`
`173color{red}{9}=>173 - color{red}{9} xx 5 = 173 -45 = 128`
`12color{red}{8}=>12 - color{red}{8} xx 5 = 12 -40 = -28`
Here -28 is not divisible by 17.
`:.` 17543 is not divisible by 17.
15. Check whether 4122 is divisible by 18 or not?
Solution:
Division rule of 18 : If number is divisible by 2 and 9, then number is also divisible by 18.
Last digit of 4122 is 2, which is divisible by 2.
`:.` 4122 is divisible by 2.
Sum of digits of 4122 is `4+1+2+2=9`, which is divisible by 9.
`:.` 4122 is divisible by 9.
4122 is divisible by 2 and 9.
`:.` 4122 is divisible by 18.
16. Check whether 4120 is divisible by 18 or not?
Solution:
Division rule of 18 : If number is divisible by 2 and 9, then number is also divisible by 18.
Last digit of 4120 is 0, which is divisible by 2.
`:.` 4120 is divisible by 2.
Sum of digits of 4120 is `4+1+2+0=7`, which is not divisible by 9.
`:.` 4120 is not divisible by 9.
Hence 4120 is also not divisible by 18.
17. Check whether 19456 is divisible by 19 or not?
Solution:
Division 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)
Check 19456 is divisible by 19 or not
`1945color{red}{6}=>1945 + color{red}{6} xx 2 = 1945 +12 = 1957`
`195color{red}{7}=>195 + color{red}{7} xx 2 = 195 +14 = 209`
`20color{red}{9}=>20 + color{red}{9} xx 2 = 20 +18 = 38`
Here 38 is divisible by 19.
`:.` 19456 is divisible by 19.
18. Check whether 19455 is divisible by 19 or not?
Solution:
Division 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)
Check 19455 is divisible by 19 or not
`1945color{red}{5}=>1945 + color{red}{5} xx 2 = 1945 +10 = 1955`
`195color{red}{5}=>195 + color{red}{5} xx 2 = 195 +10 = 205`
`20color{red}{5}=>20 + color{red}{5} xx 2 = 20 +10 = 30`
Here 30 is not divisible by 19.
`:.` 19455 is not divisible by 19.
19. Check whether 2560 is divisible by 20 or not?
Solution:
Division rule of 20 : If number is divisible by 4 and 5, then number is also divisible by 20.
Last 2 digit of 2560 is 60, which is divisible by 4.
`:.` 2560 is divisible by 4.
Last digit of 2560 is 0.
`:.` 2560 is divisible by 5.
2560 is divisible by 4 and 5.
`:.` 2560 is divisible by 20.
20. Check whether 2550 is divisible by 20 or not?
Solution:
Division rule of 20 : If number is divisible by 4 and 5, then number is also divisible by 20.
Last 2 digit of 2550 is 50, which is not divisible by 4.
`:.` 2550 is not divisible by 4.
Hence 2550 is also not divisible by 20.
This material is intended as a summary. Use your textbook for detail explanation.
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