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Last updated date: 25th Nov 2023
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MVSAT Dec 2023

Write the HCF of the smallest composite number and the smallest prime number.

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Hint: Factors of a prime number are one and the number itself. Hence the HCF could be either $1$ or the prime number.

First, we need to define the composite and prime numbers.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than $1$ and itself.
So according to the above definition, the smallest composite number is $4$.
A prime number is a natural number greater than $1$ that is not a product of two smaller natural numbers or only has two factors $1$and the number itself.
So, the smallest prime number is $2$.
HCF is the Highest common factor.
HCF for two or more numbers is the largest number that divides each one of them without leaving a remainder.
Given the numbers$4$and $2$
First, we need to find the individual factors of each number.
Factors of $4$, ${S_1} = \left\{ {1,2,4} \right\}$
Factors of $2$, ${S_2} = \left\{ {1,2} \right\}$
Common factors of$4$and $2$ are
${S_1} \cap {S_2} = \left\{ {1,2} \right\}$
The largest number in the above set is $2$.
Hence the HCF of$4$and $2$ is $2$.
Therefore, HCF of the smallest composite number and the smallest prime number is $2$.
Note: HCF is also known as the Greatest Common Measure (GCM) and Greatest Common Divisor (GCD). HCF is always less than equal to the smallest involved. Two or more prime numbers have HCF $ = 1$.