Question

The ratio of the least prime number to the least composite number is
(a) 1 : 2
(b) 2 : 3
(c) 1 : 4
(d) 1 : 3

Answer 1

Hint: We will first find the smallest prime number and then we will find the smallest composite number. And in the final step we will find out the ratio between the least prime number and the least composite number by dividing them to the smallest ratio possible.

Complete step-by-step solution:
In the question, we are asked to find out the ratio of the least prime number and the least composite number. So, first, let us see what a prime number is. A prime number is a number that is divisible only by 1 and that number itself. Examples for prime numbers are 2, 3, 5, 7, 11, etc. The number, 1 cannot be considered as a prime number as 1 has only one factor that is, the number 1 itself. And we know that prime numbers are those which have 2 factors that is 1 and the number itself. So, we know that 1 is not a prime number. Hence, we get the least prime number as 2.
Now, let us see what a composite number is. A composite number is a number which has more than 2 factors. For example, 4, 6, 8, 9, 10, 12, etc. are composite numbers. Negative numbers are not considered as prime or composite numbers, so here we will neglect the negative numbers. We also know that 0 is neither a prime number nor a composite number. Also, 1 is neither a prime number nor a composite number. Hence we get 4 as the smallest composite number whose factors are 1, 2 and 4.
Now we have to find the ratio of the least prime number to the least composite number. We get,
$\dfrac{\text{least prime number}}{\text{least composite number}}=\dfrac{2}{4}$
On dividing the numerator and the denominator with 2, we get the ratio as 1:2.
Therefore, the ratio of the least prime number to the least composite number is 1:2. Thus option (a) is the correct answer.

Note: Prime numbers are used in secured encryption of data and it is also used in industries in fitting a number of blades in turbines. In these types of questions, students often make mistakes by considering 1 as a prime number and hence, take the value of the least prime number as 1 and end up writing the ratio as 1:4 which is wrong. So students must always keep in mind that 1 is neither a prime number nor a composite number in order to avoid such mistakes.