Question

A rabbit is packing lunches for his children. He has 90 carrots and 72 leaves of lettuce. If he is giving each bunny the same number of carrots and the same number of leaves of lettuce, how many baby bunnies must he have? He will have no extra vegetables after he packs the lunches. Responses 9 9 - no response given 3 3 - no response given 18 18 - no response given 6

Answer 1

To determine how many baby bunnies the rabbit has, we need to find the greatest common divisor (GCD) of the number of carrots (90) and the number of leaves of lettuce (72). This will tell us how many baby bunnies he can equally distribute the vegetables to, with none left over.

First, let's find the GCD of 90 and 72.

**Step 1: Find the prime factorization of 90 and 72.**

- The prime factorization of 90:
- 90 = 2 × 45
- 45 = 3 × 15
- 15 = 3 × 5
- Thus, 90 = 2 × 3² × 5

- The prime factorization of 72:
- 72 = 8 × 9
- 8 = 2³
- 9 = 3²
- Thus, 72 = 2³ × 3²

**Step 2: Identify the common prime factors and the lowest powers.**

- Both numbers have the factors 2 and 3.
- The lowest power of 2 in both factorizations is 2¹ (from 90).
- The lowest power of 3 in both factorizations is 3².

**Step 3: Multiply the common prime factors with their lowest powers.**

GCD(90, 72) = 2¹ × 3²
GCD = 2 × 9 = 18

So, the greatest common divisor, which represents the number of baby bunnies, is **18**.

Thus, the rabbit must have **18 baby bunnies**.