2. Examples (Divisibility test of 2 to 10)
1. Check whether 84 is divisible by 2 or not?
Solution:
Division rule of 2 : The last digit is even, then number is divisible by 2.
Last digit of 84 is 4, which is divisible by 2.
`:.` 84 is divisible by 2.
2. Check whether 85 is divisible by 2 or not?
Solution:
Division rule of 2 : The last digit is even, then number is divisible by 2.
Last digit of 85 is 5, which is not divisible by 2.
`:.` 85 is not divisible by 2.
3. Check whether 192 is divisible by 3 or not?
Solution:
Division rule of 3 : The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 192 is `1+9+2=12`, which is divisible by 3.
`:.` 192 is divisible by 3.
4. Check whether 193 is divisible by 3 or not?
Solution:
Division rule of 3 : The sum of the digits is divisible by 3, then number is also divisible by 3.
Sum of digits of 193 is `1+9+3=13`, which is not divisible by 3.
`:.` 193 is not divisible by 3.
5. Check whether 324 is divisible by 4 or not?
Solution:
Division rule of 4 : The last two digit is divisible by 4, then number is also divisible by 4.
Last 2 digit of 324 is 24, which is divisible by 4.
`:.` 324 is divisible by 4.
6. Check whether 322 is divisible by 4 or not?
Solution:
Division rule of 4 : The last two digit is divisible by 4, then number is also divisible by 4.
Last 2 digit of 322 is 22, which is not divisible by 4.
`:.` 322 is not divisible by 4.
7. Check whether 220 is divisible by 5 or not?
Solution:
Division rule of 5 : The last digit is 0 or 5, then number is also divisible by 5.
Last digit of 220 is 0.
`:.` 220 is divisible by 5.
8. Check whether 221 is divisible by 5 or not?
Solution:
Division rule of 5 : The last digit is 0 or 5, then number is also divisible by 5.
Last digit of 221 is 1.
`:.` 221 is not divisible by 5.
9. Check whether 1734 is divisible by 6 or not?
Solution:
Division rule of 6 : If number is divisible by 2 and 3, then number is also divisible by 6.
Last digit of 1734 is 4, which is divisible by 2.
`:.` 1734 is divisible by 2.
Sum of digits of 1734 is `1+7+3+4=15`, which is divisible by 3.
`:.` 1734 is divisible by 3.
1734 is divisible by 2 and 3.
`:.` 1734 is divisible by 6.
10. Check whether 1732 is divisible by 6 or not?
Solution:
Division rule of 6 : If number is divisible by 2 and 3, then number is also divisible by 6.
Last digit of 1732 is 2, which is divisible by 2.
`:.` 1732 is divisible by 2.
Sum of digits of 1732 is `1+7+3+2=13`, which is not divisible by 3.
`:.` 1732 is not divisible by 3.
Hence 1732 is also not divisible by 6.
11. Check whether 329 is divisible by 7 or not?
Solution:
Division rule of 7 : 2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)
Check 329 is divisible by 7 or not
`32color{red}{9}=>32 - color{red}{9} xx 2 = 32 -18 = 14`
Here 14 is divisible by 7.
`:.` 329 is divisible by 7.
12. Check whether 328 is divisible by 7 or not?
Solution:
Division rule of 7 : 2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)
Check 328 is divisible by 7 or not
`32color{red}{8}=>32 - color{red}{8} xx 2 = 32 -16 = 16`
Here 16 is not divisible by 7.
`:.` 328 is not divisible by 7.
13. Check whether 2568 is divisible by 8 or not?
Solution:
Division rule of 8 : The last three digit is divisible by 8, then number is also divisible by 8.
Last 3 digit of 2568 is 568, which is divisible by 8.
`:.` 2568 is divisible by 8.
14. Check whether 3568 is divisible by 8 or not?
Solution:
Division rule of 8 : The last three digit is divisible by 8, then number is also divisible by 8.
Last 3 digit of 3568 is 568, which is divisible by 8.
`:.` 3568 is divisible by 8.
15. Check whether 3564 is divisible by 8 or not?
Solution:
Division rule of 8 : The last three digit is divisible by 8, then number is also divisible by 8.
Last 3 digit of 3564 is 564, which is not divisible by 8.
`:.` 3564 is not divisible by 8.
16. Check whether 162 is divisible by 9 or not?
Solution:
Division rule of 9 : The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 162 is `1+6+2=9`, which is divisible by 9.
`:.` 162 is divisible by 9.
17. Check whether 163 is divisible by 9 or not?
Solution:
Division rule of 9 : The sum of the digits is divisible by 9, then number is also divisible by 9.
Sum of digits of 163 is `1+6+3=10`, which is not divisible by 9.
`:.` 163 is not divisible by 9.
18. Check whether 430 is divisible by 10 or not?
Solution:
Division rule of 10 : The last digit is 0, then number is also divisible by 10.
Last digit of 430 is 0.
`:.` 430 is divisible by 10.
19. Check whether 431 is divisible by 10 or not?
Solution:
Division rule of 10 : The last digit is 0, then number is also divisible by 10.
Last digit of 431 is 1.
`:.` 431 is not divisible by 10.
This material is intended as a summary. Use your textbook for detail explanation.
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