Q. 8

Question

In the following exercises, find the greatest common factor.

$27 p^{2} q^{3}, 45 p^{3} q^{4}, 9 p^{4} q^{3}$

Step-by-Step Solution

Verified

Answer

The GCF of the given expressions is $9 p^{2} q^{3}$ .

1Step 1. Given Information

The given expressions are $27 p^{2} q^{3}, 45 p^{3} q^{4}, 9 p^{4} q^{3}$ .

2Step 2. Factoring

Factor each of the given expressions.

$27 p^{2} q^{3} = 3 \cdot 3 \cdot 3 \cdot p \cdot p \cdot q \cdot q \cdot q 45 p^{3} q^{4} = 3 \cdot 3 \cdot 5 \cdot p \cdot p \cdot p \cdot q \cdot q \cdot q \cdot q 9 p^{4} q^{3} = 3 \cdot 3 \cdot p \cdot p \cdot p \cdot p \cdot q \cdot q \cdot q$

From the factors of the given expression, it is observed that the common factors are $3, 3, p, p, q, q, q$ .
Multiply the common factors to determine the GCF of the given expressions.

$3 \cdot 3 \cdot p \cdot p \cdot q \cdot q \cdot q = 9 p^{2} q^{3}$

So, the GCF of the given expressions is $9 p^{2} q^{3}$ .

Q. 7

Q. 9

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