HCF of Numbers and Algebraic Expressions

Find the other polynomial $q\left(x\right)$q (x) of each of the following, given that LCM and GCD and one polynomial $p\left(x\right)$ respectively. $2(x+1)(x^2-4),(x+1),(x+1)(x-2)$

Find the other polynomial $q\left(x\right)$ of the following, given that$LCM, GCD$ and one polynomial $p\left(x\right)$respectively. $\left(x^4-y^4\right)\left(x^4+x^2{y}^2+y^4\right), x^2-y^2, x^4-y^4$

The L.C.M. of $p{q}^2\left(x^2+x-20\right), p^{2}q\left(x^2-3x-4\right)$ and $p^2{q}^2\left(x^2+2x+1\right)$ is $p^2{q}^2 (x-4)(x+5){(x+1)}^2$ 

Find the HCF of $x^2+x-6, 2x^2+6x, x^2+4x+3$

Find the HCF of $9x^2-3y^2-8yz-4z^2, 4z^2-4y^2-9x^2-12xy$ and $9x^2+12xz+4z^2-4y^2$

The LCM and HCF of two polynomials are respectively ${(2a-5)}^2 (a+1)$and $(2a-5)$ If one of the polynomials is $4a^2 -20a+25$ the other one is

The product of two expressions are $(x-7)(x^2 +8x+12)$ if their H.C.F. is $(x+6)$, then find their L.C.M.

The H.C.F. and the L.C.M. of two algebraic expressions are $\left(x^2+6x+8\right)\left(x+1\right)$ and $\left(x+1\right)$ respectively. If one of the expressions is $x^2+3x+2$, then what will be the other equation?

The H.C.F. of two expressions is $x$ and their L.C.M. is $x^3-9x$. If one of the expressions is $x^2+3x$, then the other expression is

The HCF and the LCM of two algebraic expressions are $\left(a -5\right)$ and $2a^3+3a^2-44a-105$ respectively. If one of the expressions is $2a^2-3a-35$, the other will be

Find the H.C.F of the following expressions:

$20x^2{y}^2, 30y^2{z}^2, 40z^2{x}^2$

The G.C.D of $17x, 102y$ is

What is the Highest Common Factor of $2x, 3y, 5z$?

Find the G.C.D. of $a{x}^2,a^2{x}^3$ and $a^{4}x$.

There are $10$ boys and $15$ girls in a class. The teacher wants to divide the children into groups such that each group contains an equal number of boys and girls. What is the greatest number of groups that she can make like this$?$

Jose is measuring out coconut oil to Siyad and Meera. Siyed need $12$ litres of oil and Meera needs $16$ litres. Jose has jars to measure out various quantities. What is the largest jar he can use for both Siyad and Meera? (if the answer is $X$ litres, then write $X$ in the given box.)

Find the common factors and highest common factor of the number pairs given below:

$28,20$

Find the common factors and highest common factor of the number pairs given below:

$18,24$

Find the common factors and highest common factor of the number pairs given below:

$32,40$

Find the common factors and highest common factor of the number pairs given below :

$36,45$