Question

Find the common factors of the given 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) $12x=2\times 2\times 3\times x$

Factors of $12x=1,2,3,4,6,12,x$

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

Factors of $36=2,3,4,6,9,12$

Therefore, Common factors are $=2,3,4,6,12$
(ii) $2y=2\times y$

Factors of $2y=2,y$

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

Factors of $22y=2,11,22,y$

Therefore, Common factors are $=2,y,2y$
(iii) $14pq=2\times 7\times p\times q$

Factors of $14pq=2,7,14,p,q$

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

Factors of $28p^2{q}^2=2,4,7,14,28,p,q$

Therefore, Common factors are $=2,7,14,pq$
(iv) $2x=2\times x$

Factors of $2x=2,x$

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

Factors of $3x^2=3,x$

$4=2\times 2$

Factors of $4=2,4$

Therefore, Common factors are/is $=1$
(v) $6abc=6\times a\times b\times c$

Factors of $6abc=2,3,6,a,b,c$

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

Factors of $24a{b}^2=2,3,4,6,8,12,24,a,b$

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

Factors of $12a^{2}b=2,3,4,6,12,a,b$

Therefore, Common factors are $=2,3,6,ab$
(vi) $16x^3=2\times 2\times 2\times 2\times x\times x\times x$

Factors of $16x^3=2,4,8,16,x,x^2$

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

Factors of $-4x^2=-1,2,x$

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

Factors of $32x=2,4,8,16,x$

Therefore, Common factors are $=2,x,2x$
(vii) $10pq=2\times 5\times p\times q$

Factors of $10pq=2,5,p,q$

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

Factors of $20qr=2,4,5,10,q,r$

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

Factors of $30rp=2,5,3,10,6,15,30,r,p$

Therefore, Common factors are $=2,5$
(viii) $3x^2{y}^3=3\times x\times x\times y\times y\times y$

Factors of $3x^2{y}^3=3,x,y,y^2$

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

Factors of $10x^3{y}^2=2,5,x^2,y$

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

$6x^2{y}^2=2,3,x,y$

Therefore, Common factors are $=x^2{y}^2$