# What is the H.C.F. of the smallest prime number and the smallest composite number?

Last updated date: 29th Mar 2023

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Answer

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Hint: Here H.C.F. is the highest common factor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

We know that,

Smallest prime number $ = 2$

Smallest composite number $ = 4$

Prime factors of \[2\]is itself \[4\]

Now consider the prime factors of $4$

i.e. $4 = 2 \times 2$

In \[2\], there are one \[2\]while in \[4\], there are two \[2s\]. So, in this case the common factors are one \[2\].

Thus, the H.C.F. of the smallest prime number and smallest composite number is \[2\].

Note: Always remember that prime numbers start from \[2\] and composite numbers starts from \[4\]. And prime numbers have only two factors i.e. one and itself. But in case of composite numbers the factors are more than two.

We know that,

Smallest prime number $ = 2$

Smallest composite number $ = 4$

Prime factors of \[2\]is itself \[4\]

Now consider the prime factors of $4$

i.e. $4 = 2 \times 2$

In \[2\], there are one \[2\]while in \[4\], there are two \[2s\]. So, in this case the common factors are one \[2\].

Thus, the H.C.F. of the smallest prime number and smallest composite number is \[2\].

Note: Always remember that prime numbers start from \[2\] and composite numbers starts from \[4\]. And prime numbers have only two factors i.e. one and itself. But in case of composite numbers the factors are more than two.

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