Explanation
$$ {\textbf{Step - 1: Solve with example}} $$
$$ {\text{As we know Factors are all the numbers that divide a number completely, }} $$
$$ {\text{i}}{\text{.e}}{\text{., without leaving any remainder, are called factors of that number}}{\text{.}} $$
$$ {\text{Multiples are those numbers which on multiplication give the desired number}}{\text{. }} $$
$$ {\text{All these multiples individually can be named as a factor of the given number}}{\text{.}} $$
$${\textbf{Step -2: Find factors}}$$
$$ {\text{To find the factors of any given number, }} $$
$$ {\text{we express each number as a product of prime numbers since they do not leave any remainder}}{\text{.}} $$
$$ {\text{For example, consider some numbers such as 1, 8, 21, 29}}{\text{.The factor of 1 is 1}}{\text{.}} $$
$$ {\text{The factors of 8 are 1, 2, 4 and 8}}{\text{.}} $$
$$ {\text{The factors of 21 are 1, 3, 7 and 21}} $$
$$ {\text{The factors of 29 are 1 and 29}}{\text{.}} $$
$$ {\text{From the above data, we observe that - }} $$
$$ {\text{1 is the greatest factor of itself and the smallest factor of any other number}}{\text{.}} $$
$$ {\textbf{Hence, the correct answer is option B}}{\text{. }} $$
$$ {\textbf{Step - 1: Find the required answer using definition of co-prime numbers.}} $$
$$ {\text{By definition of co-prime numbers,}} $$
$$ {\text{Two numbers having only 1 as their common factor are called co-prime numbers.}} $$
$$ {\text{So, HCF of two co-prime numbers is 1.}} $$
$$ {\textbf{Hence, the correct option is A.}} $$
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