Find the GCF 16 , 48 , 52

$16$ , $48$ , $52$

Step 1

Find the common factors for the numerical part:

$16, 48, 52$

Step 2

The factors for $16$ are $1, 2, 4, 8, 16$ .

The factors for $16$ are all numbers between $1$ and $16$ , which divide $16$ evenly.

Check numbers between $1$ and $16$

Find the factor pairs of $16$ where $x \cdot y = 16$ .

$\begin{array}{c} x & y \\ 1 & 16 \\ 2 & 8 \\ 4 & 4 \end{array}$

List the factors for $16$ .

$1, 2, 4, 8, 16$

Step 3

The factors for $48$ are $1, 2, 3, 4, 6, 8, 12, 16, 24, 48$ .

The factors for $48$ are all numbers between $1$ and $48$ , which divide $48$ evenly.

Check numbers between $1$ and $48$

Find the factor pairs of $48$ where $x \cdot y = 48$ .

$\begin{array}{c} x & y \\ 1 & 48 \\ 2 & 24 \\ 3 & 16 \\ 4 & 12 \\ 6 & 8 \end{array}$

List the factors for $48$ .

$1, 2, 3, 4, 6, 8, 12, 16, 24, 48$

Step 4

The factors for $52$ are $1, 2, 4, 13, 26, 52$ .

The factors for $52$ are all numbers between $1$ and $52$ , which divide $52$ evenly.

Check numbers between $1$ and $52$

Find the factor pairs of $52$ where $x \cdot y = 52$ .

$\begin{array}{c} x & y \\ 1 & 52 \\ 2 & 26 \\ 4 & 13 \end{array}$

List the factors for $52$ .

$1, 2, 4, 13, 26, 52$

Step 5

List all the factors for $16, 48, 52$ to find the common factors.

$16$ : $1, 2, 4, 8, 16$

$48$ : $1, 2, 3, 4, 6, 8, 12, 16, 24, 48$

$52$ : $1, 2, 4, 13, 26, 52$

Step 6

The common factors for $16, 48, 52$ are $1, 2, 4$ .

$1, 2, 4$

Step 7

The GCF (HCF) of the numerical factors $1, 2, 4$ is $4$ .

$4$