Algebra Examples

26 x - 13

$26 x - 13$

Step 1

Since

26 x, - 13

$26 x, - 13$ contains both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numeric part, then find GCF for the variable part.

Steps to find the GCF for

26 x, - 13

$26 x, - 13$ :

1. Find the GCF for the numerical part

26, - 13

$26, - 13$

2. Find the GCF for the variable part

x^{1}

$x^{1}$

3. Multiply the values together

Step 2

Find the common factors for the numerical part:

26, - 13

$26, - 13$

Step 3

The factors for

26

$26$ are

1, 2, 13, 26

$1, 2, 13, 26$ .

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Step 3.1

The factors for

26

$26$ are all numbers between

1

$1$ and

26

$26$ , which divide

26

$26$ evenly.

Check numbers between

1

$1$ and

26

$26$

Step 3.2

Find the factor pairs of

26

$26$ where

x \cdot y = 26

$x \cdot y = 26$ .

\begin{array}{c} x & y \\ 1 & 26 \\ 2 & 13 \end{array}

$\begin{array}{c} x & y \\ 1 & 26 \\ 2 & 13 \end{array}$

Step 3.3

List the factors for

26

$26$ .

1, 2, 13, 26

$1, 2, 13, 26$

1, 2, 13, 26

$1, 2, 13, 26$

Step 4

The factors for

- 13

$- 13$ are

1, 13

$1, 13$ .

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Step 4.1

The factors for

- 13

$- 13$ are all numbers between

1

$1$ and

13

$13$ , which divide

- 13

$- 13$ evenly.

Check numbers between

1

$1$ and

13

$13$

Step 4.2

Find the factor pairs of

- 13

$- 13$ where

x \cdot y = - 13

$x \cdot y = - 13$ .

\begin{array}{c} x & y \\ 1 & 13 \end{array}

$\begin{array}{c} x & y \\ 1 & 13 \end{array}$

Step 4.3

List the factors for

- 13

$- 13$ .

1, 13

$1, 13$

1, 13

$1, 13$

Step 5

List all the factors for

26, - 13

$26, - 13$ to find the common factors.

26

$26$ :

1, 2, 13, 26

$1, 2, 13, 26$

- 13

$- 13$ :

1, 13

$1, 13$

Step 6

The common factors for

26, - 13

$26, - 13$ are

1, 13

$1, 13$ .

1, 13

$1, 13$

Step 7

The numbers do not contain any common variable factors. The GCF (HCF) of the numerical factors

1, 13

$1, 13$ is

13

$13$ .

13

$13$