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,
$x \times x \times y \times y$ = $x^2y^2$