Find the number of common factors of $16 x^{3}$ and $32 x$ .

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Solution

The correct option is A 10
$16 x^{3} = 2 \times 2 \times 2 \times 2 \times x \times x \times x$
$32 x = 2 \times 2 \times 2 \times 2 \times 2 \times x$

The common factors of $16 x^{3}$ and $32 x$ are 1, 2, 4, 8, 16, 𝑥, 2𝑥, 4𝑥, 8𝑥, and 16𝑥.

The total number of common factors is 10.

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16 x^{3}, - 4 x^{2}, 32 x

Find the common factors of the terms

(i) $12 x, 36$

(ii) $2 y, 22 x y$

(iii) $14 p q, 28 p^{2} q^{2}$

(iv) $2 x, 3 x^{2}, 4$

(v) $6 a b c, 24 a b^{2}, 12 a^{2} b$

(vi) $16 x^{3}, - 4 x^{2}, 32 x$

(vii) $10 p q, 20 q r, 30 r p$

(viii) $3 x^{2} y^{3}, 10 x^{3} y^{2}, 6 x^{2} y^{2} z$

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2 y, 22 x y

14 p q, 28 p^{2} q^{2}

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6 a b c, 24 a b^{2}, 12 a^{2} b

16 x^{3}, - 4 x^{2}, 32 x

10 p q, 20 q r, 30 r p

3 x^{2} y^{3}, 10 x^{3} y^{2}, 6 x^{2} y^{2} z

16 x^{3}, - 4 x^{2}, 32 x

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