Question

Find the common factors of the terms 

1. \(12x, 36\) 
2.  \(2y, 22xy\) 
3.  \(14pq, 28p ^2q ^2\) 
4.  \(2x, 3x ^2 , 4 \)
5.  \(6abc, 24ab^2 , 12a ^2b \)
6.  \(16x^ 3 , -4x ^2 , 32x \)
7.  \(10pq, 20qr, 30rp\) 
8. \(3x ^2 y ^3 , 10x^ 3 y ^2 , 6x^ 2 y ^2 z\)

Answer 1

(i) \(12x = 2 \times 2 \times 3 \times x\)
\(36\) = \(2 \times 2 \times 3 \times 3\)
The common factors are \(2, 2, 3\).
And, \(2 \times 2 \times 3 = 12\)

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(ii) \(2y = 2 x y\)
\(22xy = 2 \times 11 \times x \times y\)
The common factors are \(2, y\).
And, \(2 \times y = 2y\)

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(iii) \(14pq = 2 \times 7 \times p \times q\)
\(28p^2q^2= 2 \times 2 \times 7 \times p \times p \times q \times q\)
The common factors are \(2, 7, p, q\).
And, \(2 \times 7 \times p \times q = 14pq\)

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(iv) \(2x = 2 \times x\)
\(3x^2= 3 \times x \times x\)
\(4 = 2 \times 2\)
The common factor is \(1\).

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(v) \(6abc = 2 \times 3 \times a \times b \times c\)
\(24ab^2= 2 \times 2 \times 2 \times 3  \times a \times  b \times b\)
\(12a^2b = 2 \times 2 \times 3  \times a \times a \times b\)
The common factors are \(2, 3, a, b\).
And, \(2 \times 3 \times a \times b = 6ab\)

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(vi) \(16x^3= 2 \times 2 \times 2 \times 2 \times x \times x \times x\)
\(-4x^2 = -1 \times 2 \times 2 \times x \times x\)
\(32x = 2 \times 2 \times 2 \times 2 \times 2 \times x\)
The common factors are \(2, 2, x\).
And, \(2 \times 2 \times x = 4x\)

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(vii) \(10pq = 2 \times 5 \times p \times q\)
\(20qr = 2 \times 2 \times 5 \times q \times r\)
\(30rp = 2 \times 3 \times 5 \times r \times p\)
The common factors are \(2, 5\).
And, \(2 \times 5 = 10\)

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(viii) \(3x^2y^3 = 3 \times x \times x \times y \times y \times y\)
\(10x^3y^2= 2 \times 5 \times x \times x \times x \times y \times y\)
\(6x^2y^2z = 2 \times 3 \times x \times x \times y \times y \times z\)
The common factors are \(x, x, y, y\).
And,
\(x \times x \times y \times y\) = \(x^2y^2\)