Tristan is planting 18 bushes and 12 trees in rows. If he wants all the rows to be exactly the same, with no plants left over, what is the greatest number of rows Tristan can plant?
Question
Tristan is planting 18 bushes and 12 trees in rows. If he wants all the rows to be exactly the same, with no plants left over, what is the greatest number of rows Tristan can plant?
Solution
To find the greatest number of rows Tristan can plant, we need to determine the greatest common divisor (GCD) of 18 and 12.
Step 1: Find the prime factors of both numbers:
- The prime factors of 18 are 2 * 3 * 3.
- The prime factors of 12 are 2 * 2 * 3.
Step 2: Identify the common prime factors:
- Both 18 and 12 have a common factor of 2 and 3.
Step 3: Determine the GCD:
- The GCD is the product of the common prime factors, which is 2 * 3 = 6.
Step 4: Calculate the number of rows:
- To have all rows exactly the same, we need to divide the total number of plants (18 + 12 = 30) by the GCD (6).
- 30 divided by 6 equals 5.
Therefore, Tristan can plant a maximum of 5 rows with all rows having the same number of bushes and trees.
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