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

Question

9
3
18
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). The GCD will tell us how many baby bunnies he has, as he will share the carrots and lettuce evenly with no extras.

First, we can calculate the GCD of 90 and 72.

1. Prime factorization of 90:

   • 90 = 2 × 3^2 × 5

2. Prime factorization of 72:

   • 72 = 2^3 × 3^2

3. Finding the GCD:

   • For the base 2: The minimum exponent is 1 (from 90).
   • For the base 3: The minimum exponent is 2 (common to both).
   • For the base 5: Not present in 72.

Thus, the GCD is: GCD = 2^1 × 3^2 = 2 × 9 = 18.

This means the rabbit must have 18 baby bunnies. Therefore, the answer is:

18