By definition a prime number and a composite number are:
Prime numbers: whole numbers greater than 1, that have only two factors: 1 and the number itself.
Composite numbers: whole numbers greater than 1, that have more than two factors. It is divisible by the number itself, the number 1 and at least one other number.
In that order, 1 is not a prime number and -600 is not a composite number. Options c and e are false.
Now, we need to check 443, 541 and 591.
To check if a number is prime or composite, we have to apply divisibility tests and check if the number is divisible by 2, 5, 3, 11, 7 or 13.
The divisibility rules for these numbers are:
2: If the last digit is an even number.
These numbers are odd, then they are not divisible by 2.
3: a number is completely divisible by 3 if the sum of its digits is divisible by 3.
4+4+3=11 it is not divisible by 3
5+4+1=10 it is not divisible by 3
5+9+1=15 and 1+5=6 it is divisible by 3, then 591 is not a prime number (option d is false).
5: a number is divisible by 5 if the last digit is 0 or 5.
443 and 541 are not divisible by 5.
11: take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number:
443-> 4-4+3=3 it is not divisible by 11
541->5-4+1=2 it is not divisible by 13
13: to check if a number is divisible by 13, we have to add four times of the last digit of the number to the remaining number and repeat the process until you get a two-digit number. Now check if that two-digit number is divisible by 13 or not. If it is divisible, then the given number is divisible by 13.
44+(3*4)=44+12=56 it is not divisible by 13
54+(1*4)=54+4=58 it is not divisible by 13.
Then, 443 and 541 are both prime numbers, then the answer is b. 541 is a prime number.