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) \(3x^2y^3, 10x^3y^2, 6x^2y^2z\)


Answer :

(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 = \(x^2y^2\).

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