Find the GCF 48 , 140

$48$ , $140$

Step 1

Find the common factors for the numerical part:

$48, 140$

Step 2

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 3

The factors for $140$ are $1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140$ .

The factors for $140$ are all numbers between $1$ and $140$ , which divide $140$ evenly.

Check numbers between $1$ and $140$

Find the factor pairs of $140$ where $x \cdot y = 140$ .

$\begin{array}{c} x & y \\ 1 & 140 \\ 2 & 70 \\ 4 & 35 \\ 5 & 28 \\ 7 & 20 \\ 10 & 14 \end{array}$

List the factors for $140$ .

$1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140$

Step 4

List all the factors for $48, 140$ to find the common factors.

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

$140$ : $1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140$

Step 5

The common factors for $48, 140$ are $1, 2, 4$ .

$1, 2, 4$

Step 6

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

$4$