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?

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?

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1 point
7
10
14
28

Answer 1

To find the greatest number of arrangements, we need to find the greatest common divisor (GCD) of 21 and 28.

To do this, we can use the Euclidean algorithm.

Dividing 28 by 21, we get a quotient of 1 and a remainder of 7.

So, 28 = 21 * 1 + 7.

Now, we can divide 21 by 7, and the quotient is 3 with no remainder.

So, 21 = 7 * 3.

Since we have no remainder, the GCD of 21 and 28 is 7.

Therefore, Jill can make 7 arrangements with the same number of red roses and white roses.

The answer is 7.