Precalculus Examples

$28$ and

$42$

Step 1

Find the common factors for the numerical part:

$28, 42$

Step 2

The factors for

$28$ are

$1, 2, 4, 7, 14, 28$ .

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Step 2.1

The factors for

$28$ are all numbers between

$1$ and

$28$ , which divide

$28$ evenly.

Check numbers between

$1$ and

$28$

Step 2.2

Find the factor pairs of

$28$ where

$x \cdot y = 28$ .

$\begin{array}{c} x & y \\ 1 & 28 \\ 2 & 14 \\ 4 & 7 \end{array}$

Step 2.3

List the factors for

$28$ .

$1, 2, 4, 7, 14, 28$

Step 3

The factors for

$42$ are

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

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Step 3.1

The factors for

$42$ are all numbers between

$1$ and

$42$ , which divide

$42$ evenly.

Check numbers between

$1$ and

$42$

Step 3.2

Find the factor pairs of

$42$ where

$x \cdot y = 42$ .

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

Step 3.3

List the factors for

$42$ .

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

Step 4

List all the factors for

$28, 42$ to find the common factors.

$28$ :

$1, 2, 4, 7, 14, 28$

$42$ :

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

Step 5

The common factors for

$28, 42$ are

$1, 2, 7, 14$ .

$1, 2, 7, 14$

Step 6

The GCF (HCF) of the numerical factors

$1, 2, 7, 14$ is

$14$ .

$14$

$28$ and $42$

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