Algebra Examples

$42$ , $28$ , $70$

Step 1

Find the common factors for the numerical part:

$42, 28, 70$

Step 2

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

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Step 2.1

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

Check numbers between $1$ and $42$

Step 2.2

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 2.3

List the factors for $42$ .

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

Step 3

The factors for $28$ are $1, 2, 4, 7, 14, 28$ .

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Step 3.1

The factors for $28$ are all numbers between $1$ and $28$ , which divide $28$ evenly.

Check numbers between $1$ and $28$

Step 3.2

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 3.3

List the factors for $28$ .

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

Step 4

The factors for $70$ are $1, 2, 5, 7, 10, 14, 35, 70$ .

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Step 4.1

The factors for $70$ are all numbers between $1$ and $70$ , which divide $70$ evenly.

Check numbers between $1$ and $70$

Step 4.2

Find the factor pairs of $70$ where $x \cdot y = 70$ .

$\begin{array}{c} x & y \\ 1 & 70 \\ 2 & 35 \\ 5 & 14 \\ 7 & 10 \end{array}$

Step 4.3

List the factors for $70$ .

$1, 2, 5, 7, 10, 14, 35, 70$

Step 5

List all the factors for $42, 28, 70$ to find the common factors.

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

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

$70$ : $1, 2, 5, 7, 10, 14, 35, 70$

Step 6

The common factors for $42, 28, 70$ are $1, 2, 7, 14$ .

$1, 2, 7, 14$

Step 7

The GCF (HCF) of the numerical factors $1, 2, 7, 14$ is $14$ .

$14$