If the greatest common divisor (g.c.d.) of a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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?

Similar Questions

The decimal form of $\frac{42}{35}$ is $\ldots \ldots \ldots \ldots$

State whether the following rational number has a terminating decimal expansion or not. If it has a terminating decimal expansion,find it: $\frac{29}{343}$

On a morning walk,three persons step off together and their steps measure $40\, cm$,$42\, cm$ and $45\, cm$,respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps? (in $cm$)

$\frac{47}{500}$ has $\ldots$ digits after the decimal point in its terminating decimal expansion.

Prove that the following number is irrational: $3 \sqrt{5}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module