Algebra Examples

44

$44$ ,

64

$64$ ,

100

$100$

Step 1

Find the common factors for the numerical part:

44, 64, 100

$44, 64, 100$

Step 2

The factors for

44

$44$ are

1, 2, 4, 11, 22, 44

$1, 2, 4, 11, 22, 44$ .

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Step 2.1

The factors for

44

$44$ are all numbers between

1

$1$ and

44

$44$ , which divide

44

$44$ evenly.

Check numbers between

1

$1$ and

44

$44$

Step 2.2

Find the factor pairs of

44

$44$ where

x \cdot y = 44

$x \cdot y = 44$ .

\begin{array}{c} x & y \\ 1 & 44 \\ 2 & 22 \\ 4 & 11 \end{array}

$\begin{array}{c} x & y \\ 1 & 44 \\ 2 & 22 \\ 4 & 11 \end{array}$

Step 2.3

List the factors for

44

$44$ .

1, 2, 4, 11, 22, 44

$1, 2, 4, 11, 22, 44$

1, 2, 4, 11, 22, 44

$1, 2, 4, 11, 22, 44$

Step 3

The factors for

64

$64$ are

1, 2, 4, 8, 16, 32, 64

$1, 2, 4, 8, 16, 32, 64$ .

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Step 3.1

The factors for

64

$64$ are all numbers between

1

$1$ and

64

$64$ , which divide

64

$64$ evenly.

Check numbers between

1

$1$ and

64

$64$

Step 3.2

Find the factor pairs of

64

$64$ where

x \cdot y = 64

$x \cdot y = 64$ .

\begin{array}{c} x & y \\ 1 & 64 \\ 2 & 32 \\ 4 & 16 \\ 8 & 8 \end{array}

$\begin{array}{c} x & y \\ 1 & 64 \\ 2 & 32 \\ 4 & 16 \\ 8 & 8 \end{array}$

Step 3.3

List the factors for

64

$64$ .

1, 2, 4, 8, 16, 32, 64

$1, 2, 4, 8, 16, 32, 64$

1, 2, 4, 8, 16, 32, 64

$1, 2, 4, 8, 16, 32, 64$

Step 4

The factors for

100

$100$ are

1, 2, 4, 5, 10, 20, 25, 50, 100

$1, 2, 4, 5, 10, 20, 25, 50, 100$ .

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Step 4.1

The factors for

100

$100$ are all numbers between

1

$1$ and

100

$100$ , which divide

100

$100$ evenly.

Check numbers between

1

$1$ and

100

$100$

Step 4.2

Find the factor pairs of

100

$100$ where

x \cdot y = 100

$x \cdot y = 100$ .

\begin{array}{c} x & y \\ 1 & 100 \\ 2 & 50 \\ 4 & 25 \\ 5 & 20 \\ 10 & 10 \end{array}

$\begin{array}{c} x & y \\ 1 & 100 \\ 2 & 50 \\ 4 & 25 \\ 5 & 20 \\ 10 & 10 \end{array}$

Step 4.3

List the factors for

100

$100$ .

1, 2, 4, 5, 10, 20, 25, 50, 100

$1, 2, 4, 5, 10, 20, 25, 50, 100$

1, 2, 4, 5, 10, 20, 25, 50, 100

$1, 2, 4, 5, 10, 20, 25, 50, 100$

Step 5

List all the factors for

44, 64, 100

$44, 64, 100$ to find the common factors.

44

$44$ :

1, 2, 4, 11, 22, 44

$1, 2, 4, 11, 22, 44$

64

$64$ :

1, 2, 4, 8, 16, 32, 64

$1, 2, 4, 8, 16, 32, 64$

100

$100$ :

1, 2, 4, 5, 10, 20, 25, 50, 100

$1, 2, 4, 5, 10, 20, 25, 50, 100$

Step 6

The common factors for

44, 64, 100

$44, 64, 100$ are

1, 2, 4

$1, 2, 4$ .

1, 2, 4

$1, 2, 4$

Step 7

The GCF (HCF) of the numerical factors

1, 2, 4

$1, 2, 4$ is

4

$4$ .

4

$4$