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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