Question

Find the common factors of the terms

(i) $12x,36$

(ii) $2y,22xy$

(iii) $14pq,28p^2{q}^2$

(iv) $2x,3x^2,4$

(v) $6abc,24a{b}^2,12a^{2}b$

(vi) $16x^3,-4x^2,32x$

(vii) $10pq,20qr,30rp$

(viii) $3x^2{y}^3,10x^3{y}^2,6x^2{y}^{2}z$

Answer 1

(i) $12x=2\times 2\times 3\times x$

$36=2\times 2\times 3\times 3$

The common factors are $2,2,3.$

(ii) $2y=2\times y$

$22xy=2\times 11\times x\times y$

The common factors are $2,y.$

(iii) $14pq=2\times 7\times p\times q$

$28p^2{q}^2=2\times 2\times 7\times p\times p\times q\times q$

The common factors are $2,7,p,q.$

(iv) $2x=2\times x$​

$3x^2=3\times x\times x$

$4=2\times 2$

The common factor is $1.$

(v) $6abc=2\times 3\times a\times b\times c$

$24a{b}^2=2\times 2\times 2\times 3\times a\times b\times b$

$12a^{2}b=2\times 2\times 3\times a\times a\times b$

The common factors are $2,3,a,b.$

(vi) $16x^3=2\times 2\times 2\times 2\times x\times x\times x$​

$-4x^2=-1\times 2\times 2\times x\times x$

$32x=2\times 2\times 2\times 2\times 2\times x$

The common factors are $2,2,x.$

(vii) $10pq=2\times 5\times p\times q$

$20qr=2\times 2\times 5\times q\times r$

$30rp=2\times 3\times 5\times r\times p$

The common factors are $2,5.$

(viii) $3x^2{y}^3=3\times x\times x\times y\times y\times y$

$10x^3{y}^2=2\times 5\times x\times x\times x\times y\times y$

$6x^2{y}^{2}z=2\times 3\times x\times x\times y\times y\times z$

The common factors are $x,x,y,y.$