Find the GCF 84 , 126

$84$ , $126$

Step 1

Find the common factors for the numerical part:

$84, 126$

Step 2

The factors for $84$ are $1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$ .

The factors for $84$ are all numbers between $1$ and $84$ , which divide $84$ evenly.

Check numbers between $1$ and $84$

Find the factor pairs of $84$ where $x \cdot y = 84$ .

$\begin{array}{c} x & y \\ 1 & 84 \\ 2 & 42 \\ 3 & 28 \\ 4 & 21 \\ 6 & 14 \\ 7 & 12 \end{array}$

List the factors for $84$ .

$1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$

Step 3

The factors for $126$ are $1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126$ .

The factors for $126$ are all numbers between $1$ and $126$ , which divide $126$ evenly.

Check numbers between $1$ and $126$

Find the factor pairs of $126$ where $x \cdot y = 126$ .

$\begin{array}{c} x & y \\ 1 & 126 \\ 2 & 63 \\ 3 & 42 \\ 6 & 21 \\ 7 & 18 \\ 9 & 14 \end{array}$

List the factors for $126$ .

$1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126$

Step 4

List all the factors for $84, 126$ to find the common factors.

$84$ : $1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$

$126$ : $1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126$

Step 5

The common factors for $84, 126$ are $1, 2, 3, 6, 7, 14, 21, 42$ .

$1, 2, 3, 6, 7, 14, 21, 42$

Step 6

The GCF (HCF) of the numerical factors $1, 2, 3, 6, 7, 14, 21, 42$ is $42$ .

$42$