Question

Elizabeth is a manager at a nursery and is in charge of displaying potted trees in rows. Elizabeth has 294 citrus trees and 252 palm trees. She wants to make rows of trees so that each row has the same number of trees and each tree is in a row. If the citrus trees and the palm trees must not be mixed in the​ rows, what is the largest number of trees that she can have in a​ row?

Answer 1

The largest number of trees that Elizabeth can have in a row is 42.

Elizabeth wants to create rows of trees, each with the same number of trees, without mixing citrus and palm trees in the same row. To find the largest number of trees in a row, we need to find the greatest common divisor (GCD) of the number of citrus trees (294) and palm trees (252).

The prime factorization of 294 is 2 * 3 * 7 * 7, and the prime factorization of 252 is 2 * 2 * 3 * 3 * 7. The common factors are 2, 3, and 7. Taking the product of these common factors, we get GCD(294, 252) = 2 * 3 * 7 = 42.

Therefore, the largest number of trees that Elizabeth can have in a row is 42, ensuring that each row has the same number of trees and that the citrus and palm trees remain in separate rows.