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Karen is planting 8 bushes and 36 trees in rows. If she wants all the rows to be exactly the same, with no plants left over, what is the greatest number of rows Karen can plant?

Question

Karen is planting 8 bushes and 36 trees in rows. If she wants all the rows to be exactly the same, with no plants left over, what is the greatest number of rows Karen can plant?

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Solution

To solve this problem, we need to find the greatest common divisor (GCD) of the number of bushes (8) and the number of trees (36). The GCD is the largest number that can divide both numbers without leaving a remainder.

Here are the steps to find the GCD:

  1. List the prime factors of each number:

    • Prime factors of 8: 2, 2, 2
    • Prime factors of 36: 2, 2, 3, 3
  2. Identify the common prime factors: 2, 2

  3. Multiply the common prime factors together to find the GCD: 2 * 2 = 4

So, the greatest number of rows Karen can plant is 4.

This problem has been solved

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