1. Example-1
1. is 31 a prime number
Solution:
To check if `31` is prime, test for factors from 2 up to the square root of `31` (which is `5`)
`31-:2=15` and remainder = 1, So it is not divisible by 2
`31-:3=10` and remainder = 1, So it is not divisible by 3
`31-:5=6` and remainder = 1, So it is not divisible by 5
Since, `31` is not divisible by any prime number upto `5`.
So `31` is a prime number.
2. is 13 a prime number
Solution:
To check if `13` is prime, test for factors from 2 up to the square root of `13` (which is `3`)
`13-:2=6` and remainder = 1, So it is not divisible by 2
`13-:3=4` and remainder = 1, So it is not divisible by 3
Since, `13` is not divisible by any prime number upto `3`.
So `13` is a prime number.
3. is 61 a prime number
Solution:
To check if `61` is prime, test for factors from 2 up to the square root of `61` (which is `7`)
`61-:2=30` and remainder = 1, So it is not divisible by 2
`61-:3=20` and remainder = 1, So it is not divisible by 3
`61-:5=12` and remainder = 1, So it is not divisible by 5
`61-:7=8` and remainder = 5, So it is not divisible by 7
Since, `61` is not divisible by any prime number upto `7`.
So `61` is a prime number.
4. is 51 a prime number
Solution:
To check if `51` is prime, test for factors from 2 up to the square root of `51` (which is `7`)
`51-:2=25` and remainder = 1, So it is not divisible by 2
`51-:3=17` and remainder = 0, So it is divisible by 3
Since, `51` is divisible by `3`
So `51` is not a prime number.
5. is 91 a prime number
Solution:
To check if `91` is prime, test for factors from 2 up to the square root of `91` (which is `9`)
`91-:2=45` and remainder = 1, So it is not divisible by 2
`91-:3=30` and remainder = 1, So it is not divisible by 3
`91-:5=18` and remainder = 1, So it is not divisible by 5
`91-:7=13` and remainder = 0, So it is divisible by 7
Since, `91` is divisible by `7`
So `91` is not a prime number.
6. is 77 a prime number
Solution:
To check if `77` is prime, test for factors from 2 up to the square root of `77` (which is `8`)
`77-:2=38` and remainder = 1, So it is not divisible by 2
`77-:3=25` and remainder = 2, So it is not divisible by 3
`77-:5=15` and remainder = 2, So it is not divisible by 5
`77-:7=11` and remainder = 0, So it is divisible by 7
Since, `77` is divisible by `7`
So `77` is not a prime number.
7. is 31 a composite number
Solution:
To check if `31` is composite, test for factors from 2 up to the square root of `31` (which is `5`)
`31-:2=15` and remainder = 1, So it is not divisible by 2
`31-:3=10` and remainder = 1, So it is not divisible by 3
`31-:5=6` and remainder = 1, So it is not divisible by 5
Since, `31` is not divisible by any prime number upto `5`.
So `31` is not a composite number.
8. is 51 a composite number
Solution:
To check if `51` is composite, test for factors from 2 up to the square root of `51` (which is `7`)
`51-:2=25` and remainder = 1, So it is not divisible by 2
`51-:3=17` and remainder = 0, So it is divisible by 3
Since, `51` is divisible by `3`
So `51` is a composite number.
This material is intended as a summary. Use your textbook for detail explanation.
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