Find the GCF 36 , 54 , 78 , 87

$36$ , $54$ , $78$ , $87$

Step 1

Find the common factors for the numerical part:

$36, 54, 78, 87$

Step 2

The factors for $36$ are $1, 2, 3, 4, 6, 9, 12, 18, 36$ .

The factors for $36$ are all numbers between $1$ and $36$ , which divide $36$ evenly.

Check numbers between $1$ and $36$

Find the factor pairs of $36$ where $x \cdot y = 36$ .

$\begin{array}{c} x & y \\ 1 & 36 \\ 2 & 18 \\ 3 & 12 \\ 4 & 9 \\ 6 & 6 \end{array}$

List the factors for $36$ .

$1, 2, 3, 4, 6, 9, 12, 18, 36$

Step 3

The factors for $54$ are $1, 2, 3, 6, 9, 18, 27, 54$ .

The factors for $54$ are all numbers between $1$ and $54$ , which divide $54$ evenly.

Check numbers between $1$ and $54$

Find the factor pairs of $54$ where $x \cdot y = 54$ .

$\begin{array}{c} x & y \\ 1 & 54 \\ 2 & 27 \\ 3 & 18 \\ 6 & 9 \end{array}$

List the factors for $54$ .

$1, 2, 3, 6, 9, 18, 27, 54$

Step 4

The factors for $78$ are $1, 2, 3, 6, 13, 26, 39, 78$ .

The factors for $78$ are all numbers between $1$ and $78$ , which divide $78$ evenly.

Check numbers between $1$ and $78$

Find the factor pairs of $78$ where $x \cdot y = 78$ .

$\begin{array}{c} x & y \\ 1 & 78 \\ 2 & 39 \\ 3 & 26 \\ 6 & 13 \end{array}$

List the factors for $78$ .

$1, 2, 3, 6, 13, 26, 39, 78$

Step 5

The factors for $87$ are $1, 3, 29, 87$ .

The factors for $87$ are all numbers between $1$ and $87$ , which divide $87$ evenly.

Check numbers between $1$ and $87$

Find the factor pairs of $87$ where $x \cdot y = 87$ .

$\begin{array}{c} x & y \\ 1 & 87 \\ 3 & 29 \end{array}$

List the factors for $87$ .

$1, 3, 29, 87$

Step 6

List all the factors for $36, 54, 78, 87$ to find the common factors.

$36$ : $1, 2, 3, 4, 6, 9, 12, 18, 36$

$54$ : $1, 2, 3, 6, 9, 18, 27, 54$

$78$ : $1, 2, 3, 6, 13, 26, 39, 78$

$87$ : $1, 3, 29, 87$

Step 7

The common factors for $36, 54, 78, 87$ are $1, 3$ .

$1, 3$

Step 8

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

$3$

Find the GCF 36 , 54 , 78 , 87

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