Algebra Examples

$60$ , $120$ , $105$

Step 1

Find the common factors for the numerical part:

$60, 120, 105$

Step 2

The factors for $60$ are $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$ .

Tap for more steps...

Step 2.1

The factors for $60$ are all numbers between $1$ and $60$ , which divide $60$ evenly.

Check numbers between $1$ and $60$

Step 2.2

Find the factor pairs of $60$ where $x \cdot y = 60$ .

$\begin{array}{c} x & y \\ 1 & 60 \\ 2 & 30 \\ 3 & 20 \\ 4 & 15 \\ 5 & 12 \\ 6 & 10 \end{array}$

Step 2.3

List the factors for $60$ .

$1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

Step 3

The factors for $120$ are $1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120$ .

Tap for more steps...

Step 3.1

The factors for $120$ are all numbers between $1$ and $120$ , which divide $120$ evenly.

Check numbers between $1$ and $120$

Step 3.2

Find the factor pairs of $120$ where $x \cdot y = 120$ .

$\begin{array}{c} x & y \\ 1 & 120 \\ 2 & 60 \\ 3 & 40 \\ 4 & 30 \\ 5 & 24 \\ 6 & 20 \\ 8 & 15 \\ 10 & 12 \end{array}$

Step 3.3

List the factors for $120$ .

$1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120$

Step 4

The factors for $105$ are $1, 3, 5, 7, 15, 21, 35, 105$ .

Tap for more steps...

Step 4.1

The factors for $105$ are all numbers between $1$ and $105$ , which divide $105$ evenly.

Check numbers between $1$ and $105$

Step 4.2

Find the factor pairs of $105$ where $x \cdot y = 105$ .

$\begin{array}{c} x & y \\ 1 & 105 \\ 3 & 35 \\ 5 & 21 \\ 7 & 15 \end{array}$

Step 4.3

List the factors for $105$ .

$1, 3, 5, 7, 15, 21, 35, 105$

Step 5

List all the factors for $60, 120, 105$ to find the common factors.

$60$ : $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

$120$ : $1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120$

$105$ : $1, 3, 5, 7, 15, 21, 35, 105$

Step 6

The common factors for $60, 120, 105$ are $1, 3, 5, 15$ .

$1, 3, 5, 15$

Step 7

The GCF (HCF) of the numerical factors $1, 3, 5, 15$ is $15$ .

$15$