Find the GCF 70 , 105

$70$ , $105$

Step 1

Find the common factors for the numerical part:

$70, 105$

Step 2

The factors for $70$ are $1, 2, 5, 7, 10, 14, 35, 70$ .

The factors for $70$ are all numbers between $1$ and $70$ , which divide $70$ evenly.

Check numbers between $1$ and $70$

Find the factor pairs of $70$ where $x \cdot y = 70$ .

$\begin{array}{c} x & y \\ 1 & 70 \\ 2 & 35 \\ 5 & 14 \\ 7 & 10 \end{array}$

List the factors for $70$ .

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

Step 3

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

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

Check numbers between $1$ and $105$

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

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

List the factors for $105$ .

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

Step 4

List all the factors for $70, 105$ to find the common factors.

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

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

Step 5

The common factors for $70, 105$ are $1, 5, 7, 35$ .

$1, 5, 7, 35$

Step 6

The GCF (HCF) of the numerical factors $1, 5, 7, 35$ is $35$ .

$35$