Question

Jill has 21 red roses and 28 white roses. She wants to make arrangements of flowers that look exactly the same, with the same number of red roses and the same number of white roses in each arrangement. What is the greatest number of arrangements can she make?

Answer 1

To find the greatest number of arrangements, we need to find the greatest common factor of the number of red roses and the number of white roses. Jill has 21 red roses and 28 white roses. We can find the greatest common factor of 21 and 28 by prime factorizing each number: $21=3\cdot7$ and $28=2^{2}\cdot7$. The common factor is 7, which means that Jill can make $\boxed{7}$ arrangements with 7 red roses and 7 white roses each.