6. Examples (Divisibility test of 41 to 47)
1. Check whether 2993 is divisible by 41 or not?
Solution:
Division rule of 41 : 4 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 41, then number is also divisible by 41.
(Apply this rule to the answer again if necessary)
Check 2993 is divisible by 41 or not
`299color{red}{3}=>299 - color{red}{3} xx 4 = 299 -12 = 287`
`28color{red}{7}=>28 - color{red}{7} xx 4 = 28 -28 = 0`
Here 0 is divisible by 41.
`:.` 2993 is divisible by 41.
2. Check whether 2994 is divisible by 41 or not?
Solution:
Division rule of 41 : 4 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 41, then number is also divisible by 41.
(Apply this rule to the answer again if necessary)
Check 2994 is divisible by 41 or not
`299color{red}{4}=>299 - color{red}{4} xx 4 = 299 -16 = 283`
`28color{red}{3}=>28 - color{red}{3} xx 4 = 28 -12 = 16`
Here 16 is not divisible by 41.
`:.` 2994 is not divisible by 41.
3. Check whether 19236 is divisible by 42 or not?
Solution:
Division rule of 42 : If number is divisible by 2,3 and 7, then number is also divisible by 42.
Last digit of 19236 is 6, which is divisible by 2.
`:.` 19236 is divisible by 2.
Sum of digits of 19236 is `1+9+2+3+6=21`, which is divisible by 3.
`:.` 19236 is divisible by 3.
Check 19236 is divisible by 7 or not
`1923color{red}{6}=>1923 - color{red}{6} xx 2 = 1923 -12 = 1911`
`191color{red}{1}=>191 - color{red}{1} xx 2 = 191 -2 = 189`
`18color{red}{9}=>18 - color{red}{9} xx 2 = 18 -18 = 0`
Here 0 is divisible by 7.
`:.` 19236 is divisible by 7.
19236 is divisible by 2,3 and 7.
`:.` 19236 is divisible by 42.
4. Check whether 19230 is divisible by 42 or not?
Solution:
Division rule of 42 : If number is divisible by 2,3 and 7, then number is also divisible by 42.
Last digit of 19230 is 0, which is divisible by 2.
`:.` 19230 is divisible by 2.
Sum of digits of 19230 is `1+9+2+3+0=15`, which is divisible by 3.
`:.` 19230 is divisible by 3.
Check 19230 is divisible by 7 or not
`1923color{red}{0}=>1923 - color{red}{0} xx 2 = 1923 = 1923`
`192color{red}{3}=>192 - color{red}{3} xx 2 = 192 -6 = 186`
`18color{red}{6}=>18 - color{red}{6} xx 2 = 18 -12 = 6`
Here 6 is not divisible by 7.
`:.` 19230 is not divisible by 7.
Hence 19230 is also not divisible by 42.
5. Check whether 3311 is divisible by 43 or not?
Solution:
Division rule of 43 : 13 times the last digit and add it to the rest of the number.
If the answer is divisible by 43, then number is also divisible by 43.
(Apply this rule to the answer again if necessary)
Check 3311 is divisible by 43 or not
`331color{red}{1}=>331 + color{red}{1} xx 13 = 331 +13 = 344`
`34color{red}{4}=>34 + color{red}{4} xx 13 = 34 +52 = 86`
Here 86 is divisible by 43.
`:.` 3311 is divisible by 43.
6. Check whether 3312 is divisible by 43 or not?
Solution:
Division rule of 43 : 13 times the last digit and add it to the rest of the number.
If the answer is divisible by 43, then number is also divisible by 43.
(Apply this rule to the answer again if necessary)
Check 3312 is divisible by 43 or not
`331color{red}{2}=>331 + color{red}{2} xx 13 = 331 +26 = 357`
`35color{red}{7}=>35 + color{red}{7} xx 13 = 35 +91 = 126`
`12color{red}{6}=>12 + color{red}{6} xx 13 = 12 +78 = 90`
Here 90 is not divisible by 43.
`:.` 3312 is not divisible by 43.
7. Check whether 14872 is divisible by 44 or not?
Solution:
Division rule of 44 : If number is divisible by 4 and 11, then number is also divisible by 44.
Last 2 digit of 14872 is 72, which is divisible by 4.
`:.` 14872 is divisible by 4.
Check 14872 is divisible by 11 or not
`1487color{red}{2}=>1487 - color{red}{2} = 1485`
`148color{red}{5}=>148 - color{red}{5} = 143`
`14color{red}{3}=>14 - color{red}{3} = 11`
Here 11 is divisible by 11.
`:.` 14872 is divisible by 11.
14872 is divisible by 4 and 11.
`:.` 14872 is divisible by 44.
8. Check whether 14876 is divisible by 44 or not?
Solution:
Division rule of 44 : If number is divisible by 4 and 11, then number is also divisible by 44.
Last 2 digit of 14876 is 76, which is divisible by 4.
`:.` 14876 is divisible by 4.
Check 14876 is divisible by 11 or not
`1487color{red}{6}=>1487 - color{red}{6} = 1481`
`148color{red}{1}=>148 - color{red}{1} = 147`
`14color{red}{7}=>14 - color{red}{7} = 7`
Here 7 is not divisible by 11.
`:.` 14876 is not divisible by 11.
Hence 14876 is also not divisible by 44.
9. Check whether 8055 is divisible by 45 or not?
Solution:
Division rule of 45 : If number is divisible by 9 and 5, then number is also divisible by 45.
Sum of digits of 8055 is `8+0+5+5=18`, which is divisible by 9.
`:.` 8055 is divisible by 9.
Last digit of 8055 is 5, which is divisible by 5.
`:.` 8055 is divisible by 5.
8055 is divisible by 9 and 5.
`:.` 8055 is divisible by 45.
10. Check whether 8050 is divisible by 45 or not?
Solution:
Division rule of 45 : If number is divisible by 9 and 5, then number is also divisible by 45.
Sum of digits of 8050 is `8+0+5+0=13`, which is not divisible by 9.
`:.` 8050 is not divisible by 9.
Hence 8050 is also not divisible by 45.
11. Check whether 22540 is divisible by 46 or not?
Solution:
Division rule of 46 : If number is divisible by 2 and 23, then number is also divisible by 46.
Last digit of 22540 is 0, which is divisible by 2.
`:.` 22540 is divisible by 2.
Check 22540 is divisible by 23 or not
`2254color{red}{0}=>2254 + color{red}{0} xx 7 = 2254 = 2254`
`225color{red}{4}=>225 + color{red}{4} xx 7 = 225 +28 = 253`
`25color{red}{3}=>25 + color{red}{3} xx 7 = 25 +21 = 46`
Here 46 is divisible by 23.
`:.` 22540 is divisible by 23.
22540 is divisible by 2 and 23.
`:.` 22540 is divisible by 46.
12. Check whether 22541 is divisible by 46 or not?
Solution:
Division rule of 46 : If number is divisible by 2 and 23, then number is also divisible by 46.
Last digit of 22541 is 1, which is not divisible by 2.
`:.` 22541 is not divisible by 2.
Hence 22541 is also not divisible by 46.
13. Check whether 11092 is divisible by 47 or not?
Solution:
Division rule of 47 : 14 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 47, then number is also divisible by 47.
(Apply this rule to the answer again if necessary)
Check 11092 is divisible by 47 or not
`1109color{red}{2}=>1109 - color{red}{2} xx 14 = 1109 -28 = 1081`
`108color{red}{1}=>108 - color{red}{1} xx 14 = 108 -14 = 94`
Here 94 is divisible by 47.
`:.` 11092 is divisible by 47.
14. Check whether 11093 is divisible by 47 or not?
Solution:
Division rule of 47 : 14 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 47, then number is also divisible by 47.
(Apply this rule to the answer again if necessary)
Check 11093 is divisible by 47 or not
`1109color{red}{3}=>1109 - color{red}{3} xx 14 = 1109 -42 = 1067`
`106color{red}{7}=>106 - color{red}{7} xx 14 = 106 -98 = 8`
Here 8 is not divisible by 47.
`:.` 11093 is not divisible by 47.
This material is intended as a summary. Use your textbook for detail explanation.
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