Question

Find the HCF of 2000 and 2001 by FTA and verify whether they are relatively
prime or not

Answer 1

Answer:

Two consecutive numbers are co–primes.

2000 and 2001 are Co-primes.

So, HCF (2000,2001)=1

Step-by-step explanation:

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Answer 2

Answer:

$\huge\star \underline{ \boxed{ \purple{Answer}}}\star$

1

Step-by-step explanation:

Solution

$\sf\bold{H.C.F\:=\:2000}$

➝$\sf\boxed{2000}\:÷\:2$

➝$\sf\boxed{1000}\:÷\:2$

➝$\sf\boxed{500}\:÷\:2$

➝$\sf\boxed{250}\:÷\:2$

➝$\sf\boxed{125}\:÷\:5$

➝$\sf\boxed{25}\:÷\:5$

➝$\sf\boxed{5}\:÷\:5$

➝$\sf\boxed{1}$

$\sf{Here,\:at\:last\:we\:got\:1,\:which\:means}$

$\sf{2000\:is\:completely\:divisible.}$

$\sf{And\:we\:can\:see\:that\:it\:is\:having\:more}$

$\sf{Than\:1\:factor.}$

$\sf\bold{H.C.F\:=\:2001}$

➝$\sf\boxed{2001}$

➝$\sf\boxed{1}$

$\sf{H.C.F\:of\:2001\:is\:also\:1\:but\:it\:is\:not}$

$\sf{having\:more\:than\:1\:factor.}$

Hence,

$\sf{The\:H.C.F\:of\:\boxed{2000}\:and\:\boxed{2001}\:=\:\boxed{1}}$

Two integers are relatively prime when there are no common factors other than 1.

This means that no other integer could divide both numbers evenly.

Two integers a,b are called relatively prime to each other if gcd(a,b)=1

$\sf{Since,\:here\:also\:common\:factor\:is\:1}$

$\sf{So,\:these\:no.s\:are\:relatively\:prime}$