During a brazilian day celebration, dancers perform in groups to honor brazils independance. there are 56 dancers wearing green outfits and 42 dancers wearing yellow outfits. Each group of dancers has the same number of dancers wearing green and the same number of dancers wearing yellow. all of the dancers are in a group. What is the greatest number of groups that can be formed?

Answer 1

To find the greatest number of groups that can be formed, we need to find the greatest common divisor (GCD) of 56 and 42.

The prime factorization of 56 is 2^3 * 7.
The prime factorization of 42 is 2 * 3 * 7.

To find the GCD, we take the smallest exponent of each common prime factor:

2^1 × 7^1 = 14.

Therefore, the greatest number of groups that can be formed is 14.