1. Check whether 19045 is divisible by 65 or not?Solution:Divisibility rule of 65 :
If number is divisible by 5 and 13, then number is also divisible by 65.
Divisibility rule of 5 :
The last digit is 0 or 5, then number is also divisible by 5.
Last digit of 19045 is 5, which is divisible by 5.
`:.` 19045 is divisible by 5.
Divisibility 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)
`1904color{red}{5}=>1904 + color{red}{5} xx 4 = 1904 +20 = 1924`
`192color{red}{4}=>192 + color{red}{4} xx 4 = 192 +16 = 208`
`20color{red}{8}=>20 + color{red}{8} xx 4 = 20 +32 = 52`
Here 52 is divisible by 13.
`:.` 19045 is divisible by 13.
19045 is divisible by 5 and 13.
`:.` 19045 is divisible by 65.
2. Check whether 19825 is divisible by 65 or not?Solution:Divisibility rule of 65 :
If number is divisible by 5 and 13, then number is also divisible by 65.
Divisibility rule of 5 :
The last digit is 0 or 5, then number is also divisible by 5.
Last digit of 19825 is 5, which is divisible by 5.
`:.` 19825 is divisible by 5.
Divisibility 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)
`1982color{red}{5}=>1982 + color{red}{5} xx 4 = 1982 +20 = 2002`
`200color{red}{2}=>200 + color{red}{2} xx 4 = 200 +8 = 208`
`20color{red}{8}=>20 + color{red}{8} xx 4 = 20 +32 = 52`
Here 52 is divisible by 13.
`:.` 19825 is divisible by 13.
19825 is divisible by 5 and 13.
`:.` 19825 is divisible by 65.
3. Check whether 22945 is divisible by 65 or not?Solution:Divisibility rule of 65 :
If number is divisible by 5 and 13, then number is also divisible by 65.
Divisibility rule of 5 :
The last digit is 0 or 5, then number is also divisible by 5.
Last digit of 22945 is 5, which is divisible by 5.
`:.` 22945 is divisible by 5.
Divisibility 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)
`2294color{red}{5}=>2294 + color{red}{5} xx 4 = 2294 +20 = 2314`
`231color{red}{4}=>231 + color{red}{4} xx 4 = 231 +16 = 247`
`24color{red}{7}=>24 + color{red}{7} xx 4 = 24 +28 = 52`
Here 52 is divisible by 13.
`:.` 22945 is divisible by 13.
22945 is divisible by 5 and 13.
`:.` 22945 is divisible by 65.
4. Check whether 18604 is divisible by 65 or not?Solution:Divisibility rule of 65 :
If number is divisible by 5 and 13, then number is also divisible by 65.
Divisibility rule of 5 :
The last digit is 0 or 5, then number is also divisible by 5.
Last digit of 18604 is 4, which is not divisible by 5.
`:.` 18604 is not divisible by 5.
Hence 18604 is also not divisible by 65.
5. Check whether 20254 is divisible by 65 or not?Solution:Divisibility rule of 65 :
If number is divisible by 5 and 13, then number is also divisible by 65.
Divisibility rule of 5 :
The last digit is 0 or 5, then number is also divisible by 5.
Last digit of 20254 is 4, which is not divisible by 5.
`:.` 20254 is not divisible by 5.
Hence 20254 is also not divisible by 65.
6. Check whether 24794 is divisible by 65 or not?Solution:Divisibility rule of 65 :
If number is divisible by 5 and 13, then number is also divisible by 65.
Divisibility rule of 5 :
The last digit is 0 or 5, then number is also divisible by 5.
Last digit of 24794 is 4, which is not divisible by 5.
`:.` 24794 is not divisible by 5.
Hence 24794 is also not divisible by 65.
This material is intended as a summary. Use your textbook for detail explanation.
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