A rabbit is packing lunches for his children. He has 120 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.
The greatest common factor of 120 and 72 is 24 because the common factors of 120 and 72 are 1, 2, 3, 4, 6, and 24 and 24 is the largest of these. The rabbit could be feeding 120/24=<<120/24=5>>5 bunnies carrots
The rabbit could be feeding 72/24=<<72/24=3>>3 bunnies lettuce leaves.
This means that the rabbit must have a total of 5*3=<<5*3=15>>15 baby bunnies. Answer: \boxed{15}.
15 is not an option
Apologies for the confusion. Let's reassess the problem. Since the rabbit is giving each bunny the same number of carrots and leaves of lettuce, we need to find the common factors of 120 and 72.
The prime factorization of 120 is $2^3 \cdot 3 \cdot 5$.
The prime factorization of 72 is $2^3 \cdot 3^2$.
The common factors of 120 and 72 are $2^3 \cdot 3 = 24$.
Therefore, the rabbit must have 24 baby bunnies. Answer: $\boxed{24}$.
To find out how many baby bunnies the rabbit must have, we need to determine the factors of both the number of carrots (120) and the number of leaves of lettuce (72) that are the same.
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
From the list of factors, we can see that the common factors are 1, 2, 3, 4, 6, 8, 12, and 24.
Since the rabbit wants to give each bunny the same number of carrots and leaves of lettuce, we need to find the greatest common factor (GCF) of these common factors. The GCF is the largest number that divides both numbers evenly.
Therefore, the GCF of 120 and 72 is 24.
So, the rabbit must have 24 baby bunnies in order to give them an equal number of carrots and leaves of lettuce.
To solve this problem, we need to find the common number of carrots and leaves of lettuce that can be evenly divided among the baby bunnies.
One way to approach this is by finding the greatest common divisor (GCD) of 120 (carrots) and 72 (leaves of lettuce).
Step 1: Find the GCD of 120 and 72.
- One way to find the GCD is by listing the factors of both numbers:
- Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- From these lists, we can see that the common factors are 1, 2, 3, 4, 6, 8, 12, and 24.
- Among these common factors, the largest one is 24. Therefore, the GCD of 120 and 72 is 24.
Step 2: Determine the number of baby bunnies.
- Since each baby bunny should receive the same number of carrots and leaves of lettuce, we need to find the number of groups of 24 (the GCD) that can be formed from the available carrots and leaves of lettuce.
- 120 divided by 24 equals 5.
- 72 divided by 24 equals 3.
- So, he must have 5 baby bunnies.
Therefore, the rabbit must have 5 baby bunnies in order to evenly distribute the carrots and leaves of lettuce.