Chapter 6: Q. 8 (page 572)

In the following exercises, find the greatest common factor.
$27 p^{2} q^{3}, 45 p^{3} q^{4}, 9 p^{4} q^{3}$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given Information

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

Step 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 $9 p^{2} q^{3}$ .

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In the following exercises, find the greatest common factor.
$27 p^{2} q^{3}, 45 p^{3} q^{4}, 9 p^{4} q^{3}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factoring

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In the following exercises, find the greatest common factor. 27p2q3,45p3q4,9p4q3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factoring

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Logic and Functions

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Study anywhere. Anytime. Across all devices.

In the following exercises, find the greatest common factor.
$27 p^{2} q^{3}, 45 p^{3} q^{4}, 9 p^{4} q^{3}$