Question

The numbers, which have only two factors (1 and the number itself) are called as ________.
A) composite
B) even
C) prime
D) none

Answer 1

Hint: First, we will use the concept of even numbers, composite numbers and prime numbers and then find the prime factorization of any of the numbers from them.
Then use the given condition to find the required value.

Complete step by step solution: We are given the numbers which have only two factors, 1 and the number itself.

We know that a composite number is a positive integer that can be formed by multiplying two smaller positive integers.

Let us choose a composite number randomly.

Take a composite number 18.

Finding the prime factorization of this composite number, we get

 $18=2 \times 3 \times 3$

Since it has more than two factors other than 1, so the composite number is not the correct answer.

We also know that an even number is an integer, which is divisible by two.

Let us now choose an even number randomly.

Take an even number 10.

Finding the prime factorization of this even number, we get

$10=2 \times 5$

Since it has more than two factors other than 1, so the even number is not the correct answer.

We know that a prime number is a number, which is only divisible by itself and 1.

Let us choose a prime number randomly.

Take a prime number 5.

Finding the prime factorization of this prime number, we get

$5=1 \times 5$

Since it has only two factors, the number 1 and itself, we can take any prime number to see that a prime number is a number, which is only divisible by itself and 1, the prime number is a correct option.

Therefore, the numbers that have only two factors (1 and the number itself) are called prime.

Hence, the option C is correct.

Note: In solving these types of questions, you should be familiar with the concept of prime numbers, composite numbers and even numbers. Then use the given conditions and values given in the question, and find the required answer. Also, we are supposed to write the values properly to avoid any miscalculation.