Pre-Algebra Examples

42

$42$ ,

66

$66$

Step 1

Find the common factors for the numerical part:

42, 66

$42, 66$

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

66

$66$ are

1, 2, 3, 6, 11, 22, 33, 66

$1, 2, 3, 6, 11, 22, 33, 66$ .

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Step 3.1

The factors for

66

$66$ are all numbers between

1

$1$ and

66

$66$ , which divide

66

$66$ evenly.

Check numbers between

1

$1$ and

66

$66$

Step 3.2

Find the factor pairs of

66

$66$ where

x \cdot y = 66

$x \cdot y = 66$ .

\begin{array}{c} x & y \\ 1 & 66 \\ 2 & 33 \\ 3 & 22 \\ 6 & 11 \end{array}

$\begin{array}{c} x & y \\ 1 & 66 \\ 2 & 33 \\ 3 & 22 \\ 6 & 11 \end{array}$

Step 3.3

List the factors for

66

$66$ .

1, 2, 3, 6, 11, 22, 33, 66

$1, 2, 3, 6, 11, 22, 33, 66$

1, 2, 3, 6, 11, 22, 33, 66

$1, 2, 3, 6, 11, 22, 33, 66$

Step 4

List all the factors for

42, 66

$42, 66$ to find the common factors.

42

$42$ :

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

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

66

$66$ :

1, 2, 3, 6, 11, 22, 33, 66

$1, 2, 3, 6, 11, 22, 33, 66$

Step 5

The common factors for

42, 66

$42, 66$ are

1, 2, 3, 6

$1, 2, 3, 6$ .

1, 2, 3, 6

$1, 2, 3, 6$

Step 6

The GCF (HCF) of the numerical factors

1, 2, 3, 6

$1, 2, 3, 6$ is

6

$6$ .

6

$6$