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A florist has 24 tulips and 36 carnations. If the florist wants to create identical bouquets without any leftover flowers, what is the greatest number of bouquets the florist can make?

Question

A florist has 24 tulips and 36 carnations. If the florist wants to create identical bouquets without any leftover flowers, what is the greatest number of bouquets the florist can make?

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Solution

To solve this problem, we need to find the greatest common divisor (GCD) of the two numbers, 24 (the number of tulips) and 36 (the number of carnations). The GCD is the largest number that can divide both numbers without leaving a remainder.

Here are the steps to find the GCD of 24 and 36:

  1. List the prime factors of each number:

    • The prime factors of 24 are 2, 2, 2, and 3.
    • The prime factors of 36 are 2, 2, 3, and 3.

  2. Identify the common prime factors:

    • The common prime factors are 2, 2, and 3.

  3. Multiply the common prime factors together to find the GCD:

    • 2 * 2 * 3 = 12

So, the greatest number of identical bouquets the florist can make is 12.

This problem has been solved

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