Question

HCF of $x^6{y}^4{z}^2$, $x^5{y}^4{z}^6$ and $x^7{y}^9{z}^4$ is $x^a{y}^b{z}^c$. Then a-b-c+2 = ___

Answer 1

Given expressions $x^6{y}^4{z}^2$, $x^5{y}^4{z}^6$ and $x^7{y}^9{z}^4$

Power of 'x' which divides all expressions 5

Power of 'y' which divides all expressions 4

Power of 'z' which divides all expressions 2

HCF $x^a{y}^b{z}^c$ = $x^5{y}^4{z}^2$

$a=5,b=4,c=2$

$\therefore a-b-c+2=5-4-2+2=1$