# Question 32c43

Jul 3, 2017

GCF = 6

#### Explanation:

First, list out the factors for each number (a factor is a number that goes evenly into another number).

Factors of $12 :$$1 , 2 , 3 , 4 , \textcolor{red}{6} , 12$
Factors of $30 :$$1 , 2 , 3 , 5 , \textcolor{red}{6} , 10 , 15 , 30$
Factors of $42 :$$1 , 2 , 3 , \textcolor{red}{6} , 7 , 14 , 21 , 42$

12, 30, and 42 all have the factors 1, 2, 3, and 6 in common. The largest of these common factors (greatest common factor) is 6.

Hope this helps!

Jul 8, 2017

$G C F = 2 \times 3 = 6$

#### Explanation:

Write each number as the product of its prime factors:

$\text{ } 12 = \textcolor{b l u e}{2} \times 2 \times \textcolor{red}{3}$
$\text{ "30=color(blue)(2)" } \times \textcolor{red}{3} \times 5$
" "42 = ul(color(blue)(2)" "xxcolor(red)(3)" "7)#
$G C F = \textcolor{b l u e}{2} \text{ } \times \textcolor{red}{3} = 6$

Identify which factors are common $\left(2 \mathmr{and} 3\right)$

Multiply them together to find the GCF.

$12 , 30 \mathmr{and} 42$ all divide by $6$