4. Examples (Divisibility test of 21 to 30)
1. Check whether 6069 is divisible by 21 or not?
Solution:
Division rule of 21 : If number is divisible by 3 and 7, then number is also divisible by 21.
Sum of digits of 6069 is `6+0+6+9=21`, which is divisible by 3.
`:.` 6069 is divisible by 3.
Check 6069 is divisible by 7 or not
`606color{red}{9}=>606 - color{red}{9} xx 2 = 606 -18 = 588`
`58color{red}{8}=>58 - color{red}{8} xx 2 = 58 -16 = 42`
Here 42 is divisible by 7.
`:.` 6069 is divisible by 7.
6069 is divisible by 3 and 7.
`:.` 6069 is divisible by 21.
2. Check whether 6066 is divisible by 21 or not?
Solution:
Division rule of 21 : If number is divisible by 3 and 7, then number is also divisible by 21.
Sum of digits of 6066 is `6+0+6+6=18`, which is divisible by 3.
`:.` 6066 is divisible by 3.
Check 6066 is divisible by 7 or not
`606color{red}{6}=>606 - color{red}{6} xx 2 = 606 -12 = 594`
`59color{red}{4}=>59 - color{red}{4} xx 2 = 59 -8 = 51`
Here 51 is not divisible by 7.
`:.` 6066 is not divisible by 7.
Hence 6066 is also not divisible by 21.
3. Check whether 4818 is divisible by 22 or not?
Solution:
Division rule of 22 : If number is divisible by 2 and 11, then number is also divisible by 22.
Last digit of 4818 is 8, which is divisible by 2.
`:.` 4818 is divisible by 2.
Check 4818 is divisible by 11 or not
`481color{red}{8}=>481 - color{red}{8} = 473`
`47color{red}{3}=>47 - color{red}{3} = 44`
Here 44 is divisible by 11.
`:.` 4818 is divisible by 11.
4818 is divisible by 2 and 11.
`:.` 4818 is divisible by 22.
4. Check whether 4816 is divisible by 22 or not?
Solution:
Division rule of 22 : If number is divisible by 2 and 11, then number is also divisible by 22.
Last digit of 4816 is 6, which is divisible by 2.
`:.` 4816 is divisible by 2.
Check 4816 is divisible by 11 or not
`481color{red}{6}=>481 - color{red}{6} = 475`
`47color{red}{5}=>47 - color{red}{5} = 42`
Here 42 is not divisible by 11.
`:.` 4816 is not divisible by 11.
Hence 4816 is also not divisible by 22.
5. Check whether 29946 is divisible by 23 or not?
Solution:
Division rule of 23 : 7 times the last digit and add it to the rest of the number.
If the answer is divisible by 23, then number is also divisible by 23.
(Apply this rule to the answer again if necessary)
Check 29946 is divisible by 23 or not
`2994color{red}{6}=>2994 + color{red}{6} xx 7 = 2994 +42 = 3036`
`303color{red}{6}=>303 + color{red}{6} xx 7 = 303 +42 = 345`
`34color{red}{5}=>34 + color{red}{5} xx 7 = 34 +35 = 69`
Here 69 is divisible by 23.
`:.` 29946 is divisible by 23.
6. Check whether 29945 is divisible by 23 or not?
Solution:
Division rule of 23 : 7 times the last digit and add it to the rest of the number.
If the answer is divisible by 23, then number is also divisible by 23.
(Apply this rule to the answer again if necessary)
Check 29945 is divisible by 23 or not
`2994color{red}{5}=>2994 + color{red}{5} xx 7 = 2994 +35 = 3029`
`302color{red}{9}=>302 + color{red}{9} xx 7 = 302 +63 = 365`
`36color{red}{5}=>36 + color{red}{5} xx 7 = 36 +35 = 71`
Here 71 is not divisible by 23.
`:.` 29945 is not divisible by 23.
7. Check whether 7176 is divisible by 24 or not?
Solution:
Division rule of 24 : If number is divisible by 8 and 3, then number is also divisible by 24.
Last 3 digit of 7176 is 176, which is divisible by 8.
`:.` 7176 is divisible by 8.
Sum of digits of 7176 is `7+1+7+6=21`, which is divisible by 3.
`:.` 7176 is divisible by 3.
7176 is divisible by 8 and 3.
`:.` 7176 is divisible by 24.
8. Check whether 7174 is divisible by 24 or not?
Solution:
Division rule of 24 : If number is divisible by 8 and 3, then number is also divisible by 24.
Last 3 digit of 7174 is 174, which is not divisible by 8.
`:.` 7174 is not divisible by 8.
Hence 7174 is also not divisible by 24.
9. Check whether 2250 is divisible by 25 or not?
Solution:
Division rule of 25 :
Last 2 digit of 2250 is 50, which is divisible by 25.
`:.` 2250 is divisible by 25.
10. Check whether 2240 is divisible by 25 or not?
Solution:
Division rule of 25 :
Last 2 digit of 2240 is 40, which is not divisible by 25.
`:.` 2240 is not divisible by 25.
11. Check whether 5850 is divisible by 26 or not?
Solution:
Division rule of 26 : If number is divisible by 2 and 13, then number is also divisible by 26.
Last digit of 5850 is 0, which is divisible by 2.
`:.` 5850 is divisible by 2.
Check 5850 is divisible by 13 or not
`585color{red}{0}=>585 + color{red}{0} xx 4 = 585 = 585`
`58color{red}{5}=>58 + color{red}{5} xx 4 = 58 +20 = 78`
Here 78 is divisible by 13.
`:.` 5850 is divisible by 13.
5850 is divisible by 2 and 13.
`:.` 5850 is divisible by 26.
12. Check whether 5852 is divisible by 26 or not?
Solution:
Division rule of 26 : If number is divisible by 2 and 13, then number is also divisible by 26.
Last digit of 5852 is 2, which is divisible by 2.
`:.` 5852 is divisible by 2.
Check 5852 is divisible by 13 or not
`585color{red}{2}=>585 + color{red}{2} xx 4 = 585 +8 = 593`
`59color{red}{3}=>59 + color{red}{3} xx 4 = 59 +12 = 71`
Here 71 is not divisible by 13.
`:.` 5852 is not divisible by 13.
Hence 5852 is also not divisible by 26.
13. Check whether 4428 is divisible by 27 or not?
Solution:
Division rule of 27 : 8 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 27, then number is also divisible by 27.
(Apply this rule to the answer again if necessary)
Check 4428 is divisible by 27 or not
`442color{red}{8}=>442 - color{red}{8} xx 8 = 442 -64 = 378`
`37color{red}{8}=>37 - color{red}{8} xx 8 = 37 -64 = -27`
Here -27 is divisible by 27.
`:.` 4428 is divisible by 27.
14. Check whether 4427 is divisible by 27 or not?
Solution:
Division rule of 27 : 8 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 27, then number is also divisible by 27.
(Apply this rule to the answer again if necessary)
Check 4427 is divisible by 27 or not
`442color{red}{7}=>442 - color{red}{7} xx 8 = 442 -56 = 386`
`38color{red}{6}=>38 - color{red}{6} xx 8 = 38 -48 = -10`
Here -10 is not divisible by 27.
`:.` 4427 is not divisible by 27.
15. Check whether 10892 is divisible by 28 or not?
Solution:
Division rule of 28 : If number is divisible by 4 and 7, then number is also divisible by 28.
Last 2 digit of 10892 is 92, which is divisible by 4.
`:.` 10892 is divisible by 4.
Check 10892 is divisible by 7 or not
`1089color{red}{2}=>1089 - color{red}{2} xx 2 = 1089 -4 = 1085`
`108color{red}{5}=>108 - color{red}{5} xx 2 = 108 -10 = 98`
Here 98 is divisible by 7.
`:.` 10892 is divisible by 7.
10892 is divisible by 4 and 7.
`:.` 10892 is divisible by 28.
16. Check whether 10896 is divisible by 28 or not?
Solution:
Division rule of 28 : If number is divisible by 4 and 7, then number is also divisible by 28.
Last 2 digit of 10896 is 96, which is divisible by 4.
`:.` 10896 is divisible by 4.
Check 10896 is divisible by 7 or not
`1089color{red}{6}=>1089 - color{red}{6} xx 2 = 1089 -12 = 1077`
`107color{red}{7}=>107 - color{red}{7} xx 2 = 107 -14 = 93`
Here 93 is not divisible by 7.
`:.` 10896 is not divisible by 7.
Hence 10896 is also not divisible by 28.
17. Check whether 37758 is divisible by 29 or not?
Solution:
Division rule of 29 : 3 times the last digit and add it to the rest of the number.
If the answer is divisible by 29, then number is also divisible by 29.
(Apply this rule to the answer again if necessary)
Check 37758 is divisible by 29 or not
`3775color{red}{8}=>3775 + color{red}{8} xx 3 = 3775 +24 = 3799`
`379color{red}{9}=>379 + color{red}{9} xx 3 = 379 +27 = 406`
`40color{red}{6}=>40 + color{red}{6} xx 3 = 40 +18 = 58`
Here 58 is divisible by 29.
`:.` 37758 is divisible by 29.
18. Check whether 37757 is divisible by 29 or not?
Solution:
Division rule of 29 : 3 times the last digit and add it to the rest of the number.
If the answer is divisible by 29, then number is also divisible by 29.
(Apply this rule to the answer again if necessary)
Check 37757 is divisible by 29 or not
`3775color{red}{7}=>3775 + color{red}{7} xx 3 = 3775 +21 = 3796`
`379color{red}{6}=>379 + color{red}{6} xx 3 = 379 +18 = 397`
`39color{red}{7}=>39 + color{red}{7} xx 3 = 39 +21 = 60`
Here 60 is not divisible by 29.
`:.` 37757 is not divisible by 29.
19. Check whether 13200 is divisible by 30 or not?
Solution:
Division rule of 30 : If number is divisible by 2,3 and 5, then number is also divisible by 30.
Last digit of 13200 is 0, which is divisible by 2.
`:.` 13200 is divisible by 2.
Sum of digits of 13200 is `1+3+2+0+0=6`, which is divisible by 3.
`:.` 13200 is divisible by 3.
Last digit of 13200 is 0, which is divisible by 5.
`:.` 13200 is divisible by 5.
13200 is divisible by 2,3 and 5.
`:.` 13200 is divisible by 30.
20. Check whether 13220 is divisible by 30 or not?
Solution:
Division rule of 30 : If number is divisible by 2,3 and 5, then number is also divisible by 30.
Last digit of 13220 is 0, which is divisible by 2.
`:.` 13220 is divisible by 2.
Sum of digits of 13220 is `1+3+2+2+0=8`, which is not divisible by 3.
`:.` 13220 is not divisible by 3.
Hence 13220 is also not divisible by 30.
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
|
