Pre-Algebra Examples

35

$35$ ,

63

$63$ ,

84

$84$

Step 1

Find the common factors for the numerical part:

35, 63, 84

$35, 63, 84$

Step 2

The factors for

35

$35$ are

1, 5, 7, 35

$1, 5, 7, 35$ .

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Step 2.1

The factors for

35

$35$ are all numbers between

1

$1$ and

35

$35$ , which divide

35

$35$ evenly.

Check numbers between

1

$1$ and

35

$35$

Step 2.2

Find the factor pairs of

35

$35$ where

x \cdot y = 35

$x \cdot y = 35$ .

$\begin{array}{c} x & y \\ 1 & 35 \\ 5 & 7 \end{array}$

Step 2.3

List the factors for

$35$ .

$1, 5, 7, 35$

Step 3

The factors for

$63$ are

$1, 3, 7, 9, 21, 63$ .

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Step 3.1

The factors for

$63$ are all numbers between

$1$ and

$63$ , which divide

$63$ evenly.

Check numbers between

$1$ and

$63$

Step 3.2

Find the factor pairs of

$63$ where

$x \cdot y = 63$ .

$\begin{array}{c} x & y \\ 1 & 63 \\ 3 & 21 \\ 7 & 9 \end{array}$

Step 3.3

List the factors for

$63$ .

$1, 3, 7, 9, 21, 63$

Step 4

The factors for

$84$ are

$1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$ .

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Step 4.1

The factors for

$84$ are all numbers between

$1$ and

$84$ , which divide

$84$ evenly.

Check numbers between

$1$ and

$84$

Step 4.2

Find the factor pairs of

$84$ where

$x \cdot y = 84$ .

$\begin{array}{c} x & y \\ 1 & 84 \\ 2 & 42 \\ 3 & 28 \\ 4 & 21 \\ 6 & 14 \\ 7 & 12 \end{array}$

Step 4.3

List the factors for

$84$ .

$1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$

Step 5

List all the factors for

$35, 63, 84$ to find the common factors.

$35$ :

$1, 5, 7, 35$

$63$ :

$1, 3, 7, 9, 21, 63$

$84$ :

$1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$

Step 6

The common factors for

$35, 63, 84$ are

$1, 7$ .

$1, 7$

Step 7

The GCF (HCF) of the numerical factors

$1, 7$ is

$7$ .

$7$