the ratio 6:21 can obtained from 2:7 by multiplying the ratio by a common factor. what is the common factor?

6/2 = 3 and 21/7 = 3, so the factor is 3

.

$${\frac{\left({\frac{{\mathtt{6}}}{{\mathtt{3}}}}\right)}{\left({\frac{{\mathtt{21}}}{{\mathtt{3}}}}\right)}} = {\frac{{\mathtt{2}}}{{\mathtt{7}}}}$$

$${\frac{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{3}}\right)}{\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{3}}\right)}} = {\frac{{\mathtt{6}}}{{\mathtt{21}}}}$$