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