Question -
Answer -
(i) 12x, 36
(2 ├Ч 2 ├Ч 3 ├Ч x) and (2 ├Ч 2 ├Ч 3 ├Ч 3)
Common factors are 2 ├Ч 2 ├Ч 3 = 12
Hence, the common factor = 12
(ii) 2y, 22xy
= (2 ├Ч y) and (2 ├Ч 11 ├Ч x ├Ч y)
Common factors are 2 ├Ч y = 2y
Hence, the common factor = 2y
(iii) 14pq, 28p2q2
= (2 ├Ч 7 ├Ч p ├Ч q) and (2 ├Ч 2 ├Ч 7 ├Ч p ├Ч p ├Ч q ├Ч q)
Common factors are 2 ├Ч 7 ├Ч p ├Ч q = 14pq
Hence, the common factor = 14pq
(iv) 2x, 3x2, 4
= (2 ├Ч x), (3 ├Ч x ├Ч x) and (2 ├Ч 2)
Common factor is 1
Hence, the common factor = 1 [тИ╡ 1 is afactor of every number]
(v) 6abc, 24ab2, 12a2b
= (2 ├Ч 3 ├Ч a ├Ч b ├Ч c), (2 ├Ч 2 ├Ч 2 ├Ч 3 ├Ч a ├Ч b ├Ч b) and (2 ├Ч 2 ├Ч 3 ├Ч a ├Ч a ├Ч b)
Common factors are 2 ├Ч 3 ├Ч a ├Ч b = 6ab
Hence, the common factor = 6ab
(vi) 16x3, -4x2, 32x
= (2 ├Ч 2 ├Ч 2 ├Ч 2 ├Ч x ├Ч x ├Ч x), -(2 ├Ч 2 ├Ч x ├Ч x), (2 ├Ч 2 ├Ч 2 ├Ч 2 ├Ч 2 ├Ч x)
Common factors are 2 ├Ч 2 ├Ч x = 4x
Hence, the common factor = 4x
(vii) 10pq, 20qr, 30rp
= (2 ├Ч 5 ├Ч p ├Ч q), (2 ├Ч 2 ├Ч 5 ├Ч q ├Ч r), (2 ├Ч 3 ├Ч 5 ├Ч r ├Ч p)
Common factors are 2 ├Ч 5 = 10
Hence, the common factor = 10
(viii) 3x2y2, 10x3y2, 6x2y2z
= (3 ├Ч x ├Ч x ├Ч y ├Ч y), (2 ├Ч 5 ├Ч x ├Ч x ├Ч x ├Ч y ├Ч y), (2 ├Ч 3 ├Ч x ├Ч x ├Ч y ├Ч y ├Ч z)
Common factors are x ├Ч x ├Ч y ├Ч y = x2y2
Hence, the common factor = x2y2.