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(C) The greatest common divisor (g.c.d.) of two integers $a$ and $b$,denoted as $d = 	ext{gcd}(a, b)$,is the largest positive integer that divides bo

Vedclass · Accepted Answer

If $c \mid a$ and $c \mid b$,then $c > d$

Vedclass · Answer

(C) The greatest common divisor (g.c.d.) of two integers $a$ and $b$,denoted as $d = 	ext{gcd}(a, b)$,is the largest positive integer that divides both $a$ and $b$.$1$. By definition,$d$ must divide both $a$ and $b$,so $d \mid a$ and $d \mid b$ is true.$2$. Any common divisor $c$ of $a$ and $b$ must be less than or equal to the greatest common divisor $d$. Thus,$c \leqslant d$ is true.$3$. By the property of the greatest common divisor,any common divisor $c$ of $a$ and $b$ must also divide their greatest common divisor $d$. Thus,$c \mid d$ is true.$4$. The statement $c > d$ is false because if $c$ is a common divisor,it cannot be strictly greater than the greatest common divisor $d$.

If the greatest common divisor (g.c.d.) of $a$ and $b$ is $d$,then which of the following statements is false?

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