1.Find the common factors of the given terms. (i) $$12x, 36$$ (ii) $$2y, 22xy$$ (iii)$$14pq, 28p^2q^2$$ (iv)$$2x, 3x^2, 4$$ (v) $$6abc, 24ab^2, 12a^2b$$ (vi) $$16x^3, -4x^2, 32x$$ (vii) $$10pq, 20qr, 30rp$$ (viii) $$3x^2y^3, 10x^3y^2, 6x^2y^2z$$

(i) Given:12x, 36

$$=(2 \times 2 \times 3 \times x) and (2 \times 2 \times3 \times 3)$$

So we have the common factors are $$2 \times 2 \times 3 = 12$$

Hence, the common factor = 12

(ii) Given that: 2y, 22xy

$$= (2 \times y) and (2 \times 11 \times x \times y)$$

We have the common factors are $$2 \times y = 2y$$

Hence, the common factor = 2y

(iii) Given that: $$14pq, 28p^2q^2$$

$$= (2 \times 7 \times p \times q) and (2 \times 2 \times 7 \times p \times p \times q \times q)$$

So, we have the common factors are $$2 \times 7 \times p \times q = 14pq$$

Hence, the common factor = 14pq

(iv) Given that:$$2x, 3x^2, 4$$

$$= (2 \times x), (3 \times x \times x)$$ and $$(2 \times 2)$$

We have the common factor as 1

Hence, the common factor = 1 [∵ 1 is a factor of every number]

(v)Given that: $$abc, 24ab^2, 12a^2b$$

$$= (2 \times 3 \times a \times b \times c), (2 \times 2 \times 2 \times 3 \times a \times b \times b)$$ and $$(2 \times 2 \times 3 \times a \times a \times b)$$

So, we have the common factors are $$2 \times 3 \times a \times b = 6ab$$

Hence, the common factor = 6ab

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

$$= (2 \times 2 \times 2 \times 2 \times x \times x \times x), -(2 \times 2 \times x \times x), (2 \times 2 \times 2 \times 2 \times 2 \times x)$$

We have the common factors are $$2 \times 2 \times x = 4x$$

Hence, the common factor = 4x

(vii)Given that: 10pq, 20qr, 30rp

$$= (2 \times 5 \times p \times q), (2 \times 2 \times 5 \times q \times r), (2 \times 3 \times 5 \times r \times p)$$

So,we have common factors are $$2 \times 5 = 10$$

Hence, the common factor = 10

(viii) Given that:$$3x^2y^2, 10x^3y^2, 6x^2y^2z$$

$$= (3 \times x \times x \times y \times y), (2 \times 5 \times x \times x \times x \times y \times y), (2 \times 3 \times x \times x \times y \times y \times z)$$

So, the common factors are $$x \times x \times y \times y = x^2y^2$$

Hence, the common factor = $$x^2y^2$$.