Tag: common factors and hcf

The edge of rectangular veranda are $18\ m\ 72\ cm=1872\ cm$ and $13\ m\ 20\ cm=1320\ cm$.

The two numbers which have only 1 as their common factor are called co-primes.

For example, Factors of $ 5 $  are $ 1, 5 $
Factors of $ 3 $ are $ 1, 3 $

Common factors is $ 1 $.
$ => HCF = 1 $

Prime factors of numbers are 

Since, $x^2-y^2=(x+y)(x-y)$
$x^3-y^3=(x-y)(x^2+xy+y^2)$
$H.C.F.=(x-y)$
Option A is correct.

Since, $a^2 - 25 = (a-5)(a+5) $
$ a^2 -2a -35 = a^2 -7a +5a -35 $
                         $= a(a-7)+5(a-7) $
                         $= (a+5)(a-7) $
and
$a^2+ 12a + 35 =a^2 +7a +5a +35 $
                          $=(a+7)(a+5) $
Clearly HCF of $a^2 - 25, a^2 -2a -35$ and $a^2+ 12a + 35$ i.e $ (a-5)(a+5), (a+5)(a-7)$ and $(a+7)(a+5)$ is $a+5$
Option D is correct.

$x^3 -1=(x-1)(x^2+x+1)$
$x^4+x^2+1=(x^2+x+1)(x^2-x+1)$
Clearly H.C.F of $x^3 -1$ and $x^4 + x^2 + 1$
i.e.H.C.F of $(x-1)(x^2+x+1)$ and $(x^2+x+1)(x^2-x+1)$ is  $(x^2+x+1)$
Option A is correct.

$x^2-1 = (x + 1) (x -1)$
$x^3 -1 = (x -1) (x^2 + x + 1)$
$\therefore H.C.F. = (x - 1)$
Option B is correct.

$x^3y^2=x^3\times y^2$
$x^2y^3=x^2\times y^3$
and $x^4y^4=x^4\times y^4$
$\therefore$ HCF $=x^2\times y^2=x^2y^2$.
Option C is correct.

Given the LCM two numbers 54, 90 and third number is 1890 and HCF is 18

The product of highest common factor $(H.C.F.)$ and lowest common multiple $(L.C.M.)$ of two numbers is equal to the product of two numbers.