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.(1 point)

Question

Responses

3
3

9
9

18
18

6
6

Answer 1

To find the number of baby bunnies, we need to find the greatest common factor of 90 (carrots) and 72 (lettuce leaves).

The prime factorization of 90 is 2 * 3^2 * 5.
The prime factorization of 72 is 2^3 * 3^2.

To find the greatest common factor, we find the smallest exponent for each prime factor that appears in both numbers.

The shared prime factors are 2 (which appears in both numbers with an exponent of 1) and 3 (which appears in both numbers with an exponent of 2).

Therefore, the greatest common factor is 2 * 3^2 = 18.

So, the rabbit must have 18 baby bunnies in order to divide the carrots and lettuce leaves equally.