Given:
Numbers to be checked are 437, 567, 241, 323
Concept:
Prime numbers have only two factors. one factor is the number itself and the other is 1
Explanation:
Here,
To check a number P is prime or not, select a number N such that N2 > P
And check the divisibility of P with all prime numbers below N
To check 437
For 437, N = 21 (∵ 212 = 441 > 437)
Prime numbers below 21 are 2, 3, 5, 7, 11, 13, 17, 19
Here, 19 is a factor of 437.
∴ 437 is not a Prime number
To check 567
For 567, N = 24 (∵ 242 = 576 > 567)
Prime numbers below 23 are 2, 3, 5, 7, 11, 13, 17, 19, 23
Here, 3 and 7 are factors of 567
∴ 567 is not a Prime number
To check 241
For 241, N = 16 (∵ 162 = 256 >241)
Prime numbers below 16 are 2, 3, 5, 7, 11, 13
Here, no number among 2, 3, 5, 7, 11, 13 are factors of 241
∴ 241 is a Prime number
To check for 323
For 323, N = 18 (∵ 182 = 324 > 323)
Prime numbers below 18 are 2, 3, 5, 7, 11, 13, 17
Here, 17 is a factor of 323
∴ 323 is not a Prime number
∴ Correct option is 3. 241 is a Prime number