5. Examples (Divisibility test of 31 to 40)
1. Check whether 1860 is divisible by 31 or not?
Solution:
Division rule of 31 : 3 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 31, then number is also divisible by 31.
(Apply this rule to the answer again if necessary)
Check 1860 is divisible by 31 or not
`186color{red}{0}=>186 - color{red}{0} xx 3 = 186 = 186`
`18color{red}{6}=>18 - color{red}{6} xx 3 = 18 -18 = 0`
Here 0 is divisible by 31.
`:.` 1860 is divisible by 31.
2. Check whether 1861 is divisible by 31 or not?
Solution:
Division rule of 31 : 3 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 31, then number is also divisible by 31.
(Apply this rule to the answer again if necessary)
Check 1861 is divisible by 31 or not
`186color{red}{1}=>186 - color{red}{1} xx 3 = 186 -3 = 183`
`18color{red}{3}=>18 - color{red}{3} xx 3 = 18 -9 = 9`
Here 9 is not divisible by 31.
`:.` 1861 is not divisible by 31.
3. Check whether 312032 is divisible by 32 or not?
Solution:
Division rule of 32 :
Last 5 digit of 312032 is 12032, which is divisible by 32.
`:.` 312032 is divisible by 32.
4. Check whether 312030 is divisible by 32 or not?
Solution:
Division rule of 32 :
Last 5 digit of 312030 is 12030, which is not divisible by 32.
`:.` 312030 is not divisible by 32.
5. Check whether 5280 is divisible by 33 or not?
Solution:
Division rule of 33 : If number is divisible by 3 and 11, then number is also divisible by 33.
Sum of digits of 5280 is `5+2+8+0=15`, which is divisible by 3.
`:.` 5280 is divisible by 3.
Check 5280 is divisible by 11 or not
`528color{red}{0}=>528 - color{red}{0} = 528`
`52color{red}{8}=>52 - color{red}{8} = 44`
Here 44 is divisible by 11.
`:.` 5280 is divisible by 11.
5280 is divisible by 3 and 11.
`:.` 5280 is divisible by 33.
6. Check whether 5283 is divisible by 33 or not?
Solution:
Division rule of 33 : If number is divisible by 3 and 11, then number is also divisible by 33.
Sum of digits of 5283 is `5+2+8+3=18`, which is divisible by 3.
`:.` 5283 is divisible by 3.
Check 5283 is divisible by 11 or not
`528color{red}{3}=>528 - color{red}{3} = 525`
`52color{red}{5}=>52 - color{red}{5} = 47`
Here 47 is not divisible by 11.
`:.` 5283 is not divisible by 11.
Hence 5283 is also not divisible by 33.
7. Check whether 9418 is divisible by 34 or not?
Solution:
Division rule of 34 : If number is divisible by 2 and 17, then number is also divisible by 34.
Last digit of 9418 is 8, which is divisible by 2.
`:.` 9418 is divisible by 2.
Check 9418 is divisible by 17 or not
`941color{red}{8}=>941 - color{red}{8} xx 5 = 941 -40 = 901`
`90color{red}{1}=>90 - color{red}{1} xx 5 = 90 -5 = 85`
Here 85 is divisible by 17.
`:.` 9418 is divisible by 17.
9418 is divisible by 2 and 17.
`:.` 9418 is divisible by 34.
8. Check whether 9414 is divisible by 34 or not?
Solution:
Division rule of 34 : If number is divisible by 2 and 17, then number is also divisible by 34.
Last digit of 9414 is 4, which is divisible by 2.
`:.` 9414 is divisible by 2.
Check 9414 is divisible by 17 or not
`941color{red}{4}=>941 - color{red}{4} xx 5 = 941 -20 = 921`
`92color{red}{1}=>92 - color{red}{1} xx 5 = 92 -5 = 87`
Here 87 is not divisible by 17.
`:.` 9414 is not divisible by 17.
Hence 9414 is also not divisible by 34.
9. Check whether 14420 is divisible by 35 or not?
Solution:
Division rule of 35 : If number is divisible by 5 and 7, then number is also divisible by 35.
Last digit of 14420 is 0, which is divisible by 5.
`:.` 14420 is divisible by 5.
Check 14420 is divisible by 7 or not
`1442color{red}{0}=>1442 - color{red}{0} xx 2 = 1442 = 1442`
`144color{red}{2}=>144 - color{red}{2} xx 2 = 144 -4 = 140`
`14color{red}{0}=>14 - color{red}{0} xx 2 = 14 = 14`
Here 14 is divisible by 7.
`:.` 14420 is divisible by 7.
14420 is divisible by 5 and 7.
`:.` 14420 is divisible by 35.
10. Check whether 14425 is divisible by 35 or not?
Solution:
Division rule of 35 : If number is divisible by 5 and 7, then number is also divisible by 35.
Last digit of 14425 is 5, which is divisible by 5.
`:.` 14425 is divisible by 5.
Check 14425 is divisible by 7 or not
`1442color{red}{5}=>1442 - color{red}{5} xx 2 = 1442 -10 = 1432`
`143color{red}{2}=>143 - color{red}{2} xx 2 = 143 -4 = 139`
`13color{red}{9}=>13 - color{red}{9} xx 2 = 13 -18 = -5`
Here -5 is not divisible by 7.
`:.` 14425 is not divisible by 7.
Hence 14425 is also not divisible by 35.
11. Check whether 5328 is divisible by 36 or not?
Solution:
Division rule of 36 : If number is divisible by 4 and 9, then number is also divisible by 36.
Last 2 digit of 5328 is 28, which is divisible by 4.
`:.` 5328 is divisible by 4.
Sum of digits of 5328 is `5+3+2+8=18`, which is divisible by 9.
`:.` 5328 is divisible by 9.
5328 is divisible by 4 and 9.
`:.` 5328 is divisible by 36.
12. Check whether 5326 is divisible by 36 or not?
Solution:
Division rule of 36 : If number is divisible by 4 and 9, then number is also divisible by 36.
Last 2 digit of 5326 is 26, which is not divisible by 4.
`:.` 5326 is not divisible by 4.
Hence 5326 is also not divisible by 36.
13. Check whether 1591 is divisible by 37 or not?
Solution:
Division rule of 37 : 11 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 37, then number is also divisible by 37.
(Apply this rule to the answer again if necessary)
Check 1591 is divisible by 37 or not
`159color{red}{1}=>159 - color{red}{1} xx 11 = 159 -11 = 148`
`14color{red}{8}=>14 - color{red}{8} xx 11 = 14 -88 = -74`
Here -74 is divisible by 37.
`:.` 1591 is divisible by 37.
14. Check whether 1592 is divisible by 37 or not?
Solution:
Division rule of 37 : 11 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 37, then number is also divisible by 37.
(Apply this rule to the answer again if necessary)
Check 1592 is divisible by 37 or not
`159color{red}{2}=>159 - color{red}{2} xx 11 = 159 -22 = 137`
`13color{red}{7}=>13 - color{red}{7} xx 11 = 13 -77 = -64`
Here -64 is not divisible by 37.
`:.` 1592 is not divisible by 37.
15. Check whether 16112 is divisible by 38 or not?
Solution:
Division rule of 38 : If number is divisible by 2 and 19, then number is also divisible by 38.
Last digit of 16112 is 2, which is divisible by 2.
`:.` 16112 is divisible by 2.
Check 16112 is divisible by 19 or not
`1611color{red}{2}=>1611 + color{red}{2} xx 2 = 1611 +4 = 1615`
`161color{red}{5}=>161 + color{red}{5} xx 2 = 161 +10 = 171`
`17color{red}{1}=>17 + color{red}{1} xx 2 = 17 +2 = 19`
Here 19 is divisible by 19.
`:.` 16112 is divisible by 19.
16112 is divisible by 2 and 19.
`:.` 16112 is divisible by 38.
16. Check whether 16110 is divisible by 38 or not?
Solution:
Division rule of 38 : If number is divisible by 2 and 19, then number is also divisible by 38.
Last digit of 16110 is 0, which is divisible by 2.
`:.` 16110 is divisible by 2.
Check 16110 is divisible by 19 or not
`1611color{red}{0}=>1611 + color{red}{0} xx 2 = 1611 = 1611`
`161color{red}{1}=>161 + color{red}{1} xx 2 = 161 +2 = 163`
`16color{red}{3}=>16 + color{red}{3} xx 2 = 16 +6 = 22`
Here 22 is not divisible by 19.
`:.` 16110 is not divisible by 19.
Hence 16110 is also not divisible by 38.
17. Check whether 17628 is divisible by 39 or not?
Solution:
Division rule of 39 : If number is divisible by 3 and 13, then number is also divisible by 39.
Sum of digits of 17628 is `1+7+6+2+8=24`, which is divisible by 3.
`:.` 17628 is divisible by 3.
Check 17628 is divisible by 13 or not
`1762color{red}{8}=>1762 + color{red}{8} xx 4 = 1762 +32 = 1794`
`179color{red}{4}=>179 + color{red}{4} xx 4 = 179 +16 = 195`
`19color{red}{5}=>19 + color{red}{5} xx 4 = 19 +20 = 39`
Here 39 is divisible by 13.
`:.` 17628 is divisible by 13.
17628 is divisible by 3 and 13.
`:.` 17628 is divisible by 39.
18. Check whether 17625 is divisible by 39 or not?
Solution:
Division rule of 39 : If number is divisible by 3 and 13, then number is also divisible by 39.
Sum of digits of 17625 is `1+7+6+2+5=21`, which is divisible by 3.
`:.` 17625 is divisible by 3.
Check 17625 is divisible by 13 or not
`1762color{red}{5}=>1762 + color{red}{5} xx 4 = 1762 +20 = 1782`
`178color{red}{2}=>178 + color{red}{2} xx 4 = 178 +8 = 186`
`18color{red}{6}=>18 + color{red}{6} xx 4 = 18 +24 = 42`
Here 42 is not divisible by 13.
`:.` 17625 is not divisible by 13.
Hence 17625 is also not divisible by 39.
19. Check whether 15840 is divisible by 40 or not?
Solution:
Division rule of 40 : If number is divisible by 8 and 5, then number is also divisible by 40.
Last 3 digit of 15840 is 840, which is divisible by 8.
`:.` 15840 is divisible by 8.
Last digit of 15840 is 0, which is divisible by 5.
`:.` 15840 is divisible by 5.
15840 is divisible by 8 and 5.
`:.` 15840 is divisible by 40.
20. Check whether 15850 is divisible by 40 or not?
Solution:
Division rule of 40 : If number is divisible by 8 and 5, then number is also divisible by 40.
Last 3 digit of 15850 is 850, which is not divisible by 8.
`:.` 15850 is not divisible by 8.
Hence 15850 is also not divisible by 40.
This material is intended as a summary. Use your textbook for detail explanation.
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