Question

Find the greatest common factor of the following monomials

${x}^{2} {y}^{3} and {x}^{3} {y}^{2}$
${a}^{3} and \: {ba}^{2}$
$10 {a}^{2} {b}^{3} \: 14ab \: and \: {2a}^{3} {b}^{2}$
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Answer 1

Hey mate!!

Given:- Find the greatest common factor of the following monomials

Find:- Greatest common factor

${ \bold{ \underline{Solution:- 1) {x}^{2} {y}^{3} \: and \: {x}^{3} {y}^2{}}}}$

Factors of

$1) {x}^{2} {y}^{3} \implies{ x × x × y × y × y}$

$2) {x}^{3} {y}^{2} \implies{ x × x × x × y × y}$

So, the greatest common factors

$\implies \: {x \times x \times y \times y}$

$Ans. \implies {{x}^{2}{y}^{2}}$

${\bold{\underline{Solution:- 2) {a}^{3} \: and \: {ba}^{2}}}}$

Factors of

$1) {a}^{3} \implies a \times a \times a$

$2){ba}^{2}\implies{ba \times ba}$

So, the greatest common factors

$\implies{a \times a}$

$Ans. \implies {{a}^{2}}$

${\bold{\underline{Solution:-3)10{a}^{2} {b}^{3} \: 14ab \: and \: {2a}^{3} {b}^{2}}}}$

So, the greatest common factor

$\implies{a×b}$

$Ans. \implies{ab}$

Hope it helps you mate ✌️