Find the common factors of the terms

(i) 12*x*, 36

(ii) 2*y*, 22*xy*

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

(iv) 2*x*, 3*x* ^{2},
4

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

(vi) 16*x* ^{3},
−4*x* ^{2}, 32*x*

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

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

(i) 12*x* = 2 ×
2 × 3 ×
*x*

36 = 2 × 2 × 3 × 3

The common factors are 2, 2, 3.

And, 2 × 2 × 3 = 12

(ii) 2*y* = 2 ×
*y*

22*xy
*= 2 × 11 ×
*x* × *y*

The
common factors are 2, *y*.

And,
2 × *y* = 2*y*

(iii) 14*pq* = 2 ×
7 × *p* ×
*q*

28*p*^{2}*q*^{2}
= 2 × 2 ×
7 × *p* ×
*p* × *q* ×
*q*

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

And,
2 × 7 × *p* × *q* = 14*pq*

(iv) 2*x* = 2 ×
*x*

3*x*^{2}
= 3 × *x* ×
*x*

4 = 2 × 2

The common factor is 1.

(v) 6*abc* = 2 ×
3 × *a* ×
*b* × *c*

24*ab*^{2}
= 2 × 2 ×
2 × 3 ×
*a* × *b* ×
*b*

12*a*^{2}*b*
= 2 × 2 ×
3 × *a* ×
*a* × *b*

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

And,
2 × 3 ×* a* × *b* = 6*ab*

(vi) 16*x*^{3}
= 2 × 2 ×
2 × 2 ×
*x* × *x* ×
*x*

−4*x*^{2}
= −1 × 2 ×
2 × *x* ×
*x*

32*x*
= 2 × 2 ×
2 × 2 ×
2 × *x*

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

And,
2 × 2 × *x* = 4*x*

(vii) 10*pq* = 2 ×
5 × *p* ×
*q*

20*qr*
= 2 × 2 ×
5 × *q* ×
*r*

30*rp*
= 2 × 3 ×
5 × *r* ×
*p*

The common factors are 2, 5.

And, 2 × 5 = 10

(viii) 3*x*^{2}*y*^{3
}= 3 × *x* ×
*x *×* y* ×
*y* × *y*

10*x*^{3}*y*^{2}
= 2 × 5 ×
*x* × *x* ×
*x* × *y* ×
*y*

6*x*^{2}*y*^{2}*z*
= 2 × 3 ×
*x* × *x* ×
*y *× *y* ×
*z*

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

And,

*x
*× *x *× *y* × *y* =* x*^{2}*y*^{2}

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