Question

1. 18, 6v
2. $3x^2$, 10

1. $20y$, $14y^2$
2. $25x^2$, $25y$

1. $32u^2$, $14v^2$
2. $18m^2$, $24nm$

1. $16x^2y$, $32x$
2. $30ab^3$, $20ab^3$

1. 30, 25, 10
2. 28, 14, 21

1. 10, 4, 18
2. $10ba$, $20ba$, $28ba$

1. $8y^2$, $16xy$, $16y$
2. $28b^2$, $20ab^3$, $16b^4$

Explanation:

To solve these problems, we need to find the greatest common factor (GCF) of the given terms. The GCF is the largest number or expression that divides each term without leaving a remainder. Here, we'll solve a few of them as examples:

Problem 13: \( 18, 6v \)

Step 1: Factorize the numbers

Factorize \( 18 \): \( 18 = 2 \times 3^2 \)
Factorize \( 6v \): \( 6v = 2 \times 3 \times v \)

Step 2: Identify common factors

The common factors are \( 2 \) and \( 3 \).
Multiply the common factors: \( 2 \times 3 = 6 \)

Step 1: Factorize the coefficients and variables

Factorize \( 20y \): \( 20y = 2^2 \times 5 \times y \)
Factorize \( 14y^2 \): \( 14y^2 = 2 \times 7 \times y^2 \)

Step 2: Identify common factors

The common factors are \( 2 \) and \( y \).
Multiply the common factors: \( 2 \times y = 2y \)

Step 1: Factorize each number

Factorize \( 30 \): \( 30 = 2 \times 3 \times 5 \)
Factorize \( 25 \): \( 25 = 5^2 \)
Factorize \( 10 \): \( 10 = 2 \times 5 \)

Step 2: Identify common factors

The common factor is \( 5 \).

Answer:

The GCF of \( 18 \) and \( 6v \) is \( 6 \).

Problem 15: \( 20y, 14y^2 \)