Algebra Examples

$45$ ,

$70$ ,

$85$

Step 1

Find the common factors for the numerical part:

$45, 70, 85$

Step 2

The factors for

$45$ are

$1, 3, 5, 9, 15, 45$ .

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Step 2.1

The factors for

$45$ are all numbers between

$1$ and

$45$ , which divide

$45$ evenly.

Check numbers between

$1$ and

$45$

Step 2.2

Find the factor pairs of

$45$ where

$x \cdot y = 45$ .

$\begin{array}{c} x & y \\ 1 & 45 \\ 3 & 15 \\ 5 & 9 \end{array}$

Step 2.3

List the factors for

$45$ .

$1, 3, 5, 9, 15, 45$

Step 3

The factors for

$70$ are

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

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Step 3.1

The factors for

$70$ are all numbers between

$1$ and

$70$ , which divide

$70$ evenly.

Check numbers between

$1$ and

$70$

Step 3.2

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 3.3

List the factors for

$70$ .

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

Step 4

The factors for

$85$ are

$1, 5, 17, 85$ .

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Step 4.1

The factors for

$85$ are all numbers between

$1$ and

$85$ , which divide

$85$ evenly.

Check numbers between

$1$ and

$85$

Step 4.2

Find the factor pairs of

$85$ where

$x \cdot y = 85$ .

$\begin{array}{c} x & y \\ 1 & 85 \\ 5 & 17 \end{array}$

Step 4.3

List the factors for

$85$ .

$1, 5, 17, 85$

Step 5

List all the factors for

$45, 70, 85$ to find the common factors.

$45$ :

$1, 3, 5, 9, 15, 45$

$70$ :

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

$85$ :

$1, 5, 17, 85$

Step 6

The common factors for

$45, 70, 85$ are

$1, 5$ .

$1, 5$

Step 7

The GCF (HCF) of the numerical factors

$1, 5$ is

$5$ .

$5$