A rabbit is packing lunches for his children. He has 120 carrots and 72 leaves of lettuce. If he gives 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.
A 120
B 72
C 12
D 24
To find the number of bunnies, we need to find the greatest common divisor (GCD) of 120 and 72.
The prime factorization of 120 is 2 * 2 * 2 * 3 * 5 = 2^3 * 3 * 5.
The prime factorization of 72 is 2 * 2 * 2 * 3 * 3 = 2^3 * 3^2.
The common factors between 120 and 72 are 2^3 and 3.
Therefore, the GCD of 120 and 72 is 2^3 * 3 = 24.
The rabbit must have 24 baby bunnies. Answer: D.
To determine the number of baby bunnies, we need to find the greatest common divisor (GCD) of 120 and 72.
The GCD represents the largest number that can evenly divide both 120 and 72.
To find the GCD, we can use the Euclidean algorithm. Here's how we can find it step-by-step:
Step 1: Divide 120 by 72:
120 ÷ 72 = 1 remainder 48
Step 2: Divide 72 by 48:
72 ÷ 48 = 1 remainder 24
Step 3: Divide 48 by 24:
48 ÷ 24 = 2 remainder 0
Since the remainder is 0, we stop here.
The GCD of 120 and 72 is the last non-zero remainder obtained in the steps, which is 24.
Therefore, the rabbit must have 24 baby bunnies to give each of them the same number of carrots and leaves of lettuce.
Answer: D) 24.
To solve this problem, we need to find the factors of both 120 and 72. The factors of a number are the numbers that divide into it without leaving a remainder.
Let's start with 120.
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
Next, let's find the factors of 72.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
Now, we want to find a common factor of both numbers - a number that appears in the factor lists of both 120 and 72.
Looking at the lists, we can see that 24 is a common factor. This means that if each bunny gets 24 carrots and 24 leaves of lettuce, the rabbit will have no extra vegetables after packing the lunches.
Therefore, the answer is D) 24. The rabbit must have 24 baby bunnies.