Find the GCF 42 , 66 , 60 , 48

$42$ , $66$ , $60$ , $48$

Step 1

Find the common factors for the numerical part:

$42, 66, 60, 48$

Step 2

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

The factors for $42$ are all numbers between $1$ and $42$ , which divide $42$ evenly.

Check numbers between $1$ and $42$

Find the factor pairs of $42$ where $x \cdot y = 42$ .

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

List the factors for $42$ .

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

Step 3

The factors for $66$ are $1, 2, 3, 6, 11, 22, 33, 66$ .

The factors for $66$ are all numbers between $1$ and $66$ , which divide $66$ evenly.

Check numbers between $1$ and $66$

Find the factor pairs of $66$ where $x \cdot y = 66$ .

$\begin{array}{c} x & y \\ 1 & 66 \\ 2 & 33 \\ 3 & 22 \\ 6 & 11 \end{array}$

List the factors for $66$ .

$1, 2, 3, 6, 11, 22, 33, 66$

Step 4

The factors for $60$ are $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$ .

The factors for $60$ are all numbers between $1$ and $60$ , which divide $60$ evenly.

Check numbers between $1$ and $60$

Find the factor pairs of $60$ where $x \cdot y = 60$ .

$\begin{array}{c} x & y \\ 1 & 60 \\ 2 & 30 \\ 3 & 20 \\ 4 & 15 \\ 5 & 12 \\ 6 & 10 \end{array}$

List the factors for $60$ .

$1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

Step 5

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 6

List all the factors for $42, 66, 60, 48$ to find the common factors.

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

$66$ : $1, 2, 3, 6, 11, 22, 33, 66$

$60$ : $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

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

Step 7

The common factors for $42, 66, 60, 48$ are $1, 2, 3, 6$ .

$1, 2, 3, 6$

Step 8

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

$6$

Find the GCF 42 , 66 , 60 , 48

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