Question

1. $32u^{2}$, $14v^{2}$
2. $16x^{2}y$, $32x$
3. $30$, $25$, $10$
4. $10$, $4$, $18$
5. $8y^{2}$, $16xy$, $16y$

Explanation:

Problem 17: Find GCF of \(32u^2\) and \(14v^2\)

Step 1: Prime factorize coefficients

Prime factors of \(32\): \(32 = 2^5\)
Prime factors of \(14\): \(14 = 2 \times 7\)

Step 2: Identify common factors

The common prime factor is \(2\) (with the lowest power, which is \(1\)). There are no common variables (since \(u^2\) and \(v^2\) are distinct).

Step 3: Calculate GCF

GCF is the product of common prime factors: \(2\).

Step 1: Prime factorize coefficients

Prime factors of \(16\): \(16 = 2^4\)
Prime factors of \(32\): \(32 = 2^5\)

Step 2: Analyze variable factors

For \(x\): lowest power is \(1\) (from \(32x\)).
For \(y\): only in \(16x^2y\), so no common \(y\) factor.

Step 3: Calculate GCF

Coefficient GCF: \(2^4 = 16\)
Variable GCF: \(x^1 = x\)
Multiply: \(16 \times x = 16x\)

Step 1: Prime factorize each number

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

Step 2: Identify common factors

Common prime factor: \(5\) (lowest power is \(1\)).

Step 3: Calculate GCF

GCF is \(5\).

Answer:

\(2\)

Problem 19: Find GCF of \(16x^2y\) and \(32x\)