They are: 2 and 3.
Three
2 and 3
2 and 13.
2 and 3
-- List all the divisors (factors) of 36. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36 . -- Check over the list, and mark all the ones that are prime numbers. There are only two of them, so I'll let you handle that part.
Divisors. Primes are divisible by themselves, and one. Composite numbers also have other divisors.
An integer (call it 'x') has exactly 3 divisors if and only if it is the square of a prime number. In other words, to generate a list of integers with exactly 3 divisors, just keep squaring prime numbers. A number with 3 divisors cannot be prime (a prime number has only 2 divisors, 1 and itself). So it must be a composite number, which is a number that can be factored as a product of prime numbers (Fundamental Theorem of Arithmetic) -- i.e. a composite number must have at least one prime divisor. In the case where the number has only 3 divisors, two of them are 1 and the number itself (neither of which are prime). Therefore the third divisor must be a prime number. So the three divisors of 'x' are: 1, p, x where p is prime. Now since p is a divisor (or factor) of x, and the only other divisor besides 1 and x itself, x must equal p*p -- or x=p^2 . Obvious x can't equal p*x and if x = p*1, x=p so x is prime, or has only 2 divisors... If x = p^(3) , then x = p*p* p , or p*(p^2) ... this means that p^2 would also have to be a divisor of x, and this would contradict with x having only 3 divisors. For the same reason, x = p^(greater than 3) is also not possible. So the only possibility is that an integer with exactly 3 divisors is the square of a prime number "p". The divisors are 1, p, and p^2. I'm sure there's a simpler, more elegant way of explaining this, but it should be clear enough.
No. A prime number is a number that can only be divided by itself and 1. The first prime number is 2 - which is also the only even prime number. The prime numbers from 1 - 20 are: 2 and 3 and 5 and 7 and 11 and 13 and 17 and 19
a prime number is a natural number which has exactly two distinct natural number divisors examples 1 3 5 7 11 ( all are divided by1 and can also be divided by its self
Thet are 2 and 3
31,37 are not composite
To determine which of the numbers is a prime number, we need to check each one individually. 1: 103: 103 is a prime number because it has no divisors other than 1 and itself. In other words, it cannot be evenly divided by any other whole number. 2: 229: 229 is a prime number for the same reason as 103. It has no divisors other than 1 and 229. 3: 817: 817 is not a prime number because it can be divided evenly by numbers other than 1 and itself. Specifically, it can be divided by 17, which gives us 817 ÷ 17 = 48. So, out of the given numbers, 103 and 229 are prime numbers, while 817 is not a prime number.