Algebra Examples

42

$42$ ,

28

$28$ ,

70

$70$

Step 1

Find the common factors for the numerical part:

42, 28, 70

$42, 28, 70$

Step 2

The factors for

42

$42$ are

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

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

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Step 2.1

The factors for

42

$42$ are all numbers between

1

$1$ and

42

$42$ , which divide

42

$42$ evenly.

Check numbers between

1

$1$ and

42

$42$

Step 2.2

Find the factor pairs of

42

$42$ where

x \cdot y = 42

$x \cdot y = 42$ .

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

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

Step 2.3

List the factors for

42

$42$ .

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

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

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

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

Step 3

The factors for

28

$28$ are

1, 2, 4, 7, 14, 28

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

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Step 3.1

The factors for

28

$28$ are all numbers between

1

$1$ and

28

$28$ , which divide

28

$28$ evenly.

Check numbers between

1

$1$ and

28

$28$

Step 3.2

Find the factor pairs of

28

$28$ where

x \cdot y = 28

$x \cdot y = 28$ .

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

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

Step 3.3

List the factors for

28

$28$ .

1, 2, 4, 7, 14, 28

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

1, 2, 4, 7, 14, 28

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

Step 4

The factors for

70

$70$ are

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

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

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Step 4.1

The factors for

70

$70$ are all numbers between

1

$1$ and

70

$70$ , which divide

70

$70$ evenly.

Check numbers between

1

$1$ and

70

$70$

Step 4.2

Find the factor pairs of

70

$70$ where

x \cdot y = 70

$x \cdot y = 70$ .

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

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

Step 4.3

List the factors for

70

$70$ .

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

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

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

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

Step 5

List all the factors for

42, 28, 70

$42, 28, 70$ to find the common factors.

42

$42$ :

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

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

28

$28$ :

1, 2, 4, 7, 14, 28

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

70

$70$ :

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

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

Step 6

The common factors for

42, 28, 70

$42, 28, 70$ are

1, 2, 7, 14

$1, 2, 7, 14$ .

1, 2, 7, 14

$1, 2, 7, 14$

Step 7

The GCF (HCF) of the numerical factors

1, 2, 7, 14

$1, 2, 7, 14$ is

14

$14$ .

14

$14$