(B) Let two consecutive natural numbers be $n$ and $n+1$,where $n \in \mathbb{N}$.Any common divisor of $n$ and $n+1$ must also divide their differenc

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(B) Let two consecutive natural numbers be $n$ and $n+1$,where $n \in \mathbb{N}$.Any common divisor of $n$ and $n+1$ must also divide their difference.The difference is $(n+1) - n = 1$.The only positive divisor of $1$ is $1$.Therefore,the greatest common divisor $(\text{g.c.d.})$ of $n$ and $n+1$ is $1$.

Class 10 Mathematics Real Numbers Mix Examples - Real Numbers

Easy

The $\text{g.c.d.}$ (greatest common divisor) of any two consecutive natural numbers is:

A
$2$
B
$1$
C
$0$
D
$3$

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Class 10

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Real Numbers

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Mix Examples - Real Numbers

Prove that $\sqrt{p}+\sqrt{q}$ is irrational,where $p$ and $q$ are distinct prime numbers.

Medium

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Express $96$ as a product of prime factors.

Easy

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What is the largest number that divides $626$,$3127$,and $15628$ and leaves remainders $1$,$2$,and $3$ respectively?

Medium

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Prove that,if $a$ and $b$ are odd positive integers,then $a^{2} + b^{2}$ is even but not divisible by $4$.

Difficult

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Prove that the cube of any positive integer is of the form $9m$,$9m+1$,or $9m+8$,where $m$ is an integer.

Difficult

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The $\text{g.c.d.}$ (greatest common divisor) of any two consecutive natural numbers is:

Similar Questions

Prove that $\sqrt{p}+\sqrt{q}$ is irrational,where $p$ and $q$ are distinct prime numbers.

Express $96$ as a product of prime factors.

What is the largest number that divides $626$,$3127$,and $15628$ and leaves remainders $1$,$2$,and $3$ respectively?

Prove that,if $a$ and $b$ are odd positive integers,then $a^{2} + b^{2}$ is even but not divisible by $4$.

Prove that the cube of any positive integer is of the form $9m$,$9m+1$,or $9m+8$,where $m$ is an integer.

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