Find the GCF 24 , 14 , 35

$24$ , $14$ , $35$

Step 1

Find the common factors for the numerical part:

$24, 14, 35$

Step 2

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

The factors for $24$ are all numbers between $1$ and $24$ , which divide $24$ evenly.

Check numbers between $1$ and $24$

Find the factor pairs of $24$ where $x \cdot y = 24$ .

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

List the factors for $24$ .

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

Step 3

The factors for $14$ are $1, 2, 7, 14$ .

The factors for $14$ are all numbers between $1$ and $14$ , which divide $14$ evenly.

Check numbers between $1$ and $14$

Find the factor pairs of $14$ where $x \cdot y = 14$ .

$\begin{array}{c} x & y \\ 1 & 14 \\ 2 & 7 \end{array}$

List the factors for $14$ .

$1, 2, 7, 14$

Step 4

The factors for $35$ are $1, 5, 7, 35$ .

The factors for $35$ are all numbers between $1$ and $35$ , which divide $35$ evenly.

Check numbers between $1$ and $35$

Find the factor pairs of $35$ where $x \cdot y = 35$ .

$\begin{array}{c} x & y \\ 1 & 35 \\ 5 & 7 \end{array}$

List the factors for $35$ .

$1, 5, 7, 35$

Step 5

List all the factors for $24, 14, 35$ to find the common factors.

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

$14$ : $1, 2, 7, 14$

$35$ : $1, 5, 7, 35$

Step 6

The common factors for $24, 14, 35$ are $1$ .

$1$

Step 7

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

$1$