Greatest Common Factor Quick Check
2 of 52 of 5 Items
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.(1 point)
Responses
6
6
9
9
18
18
3
The greatest common factor of 90 and 72 is 18. Therefore, the rabbit must have 18 baby bunnies.
To find the number of baby bunnies, we need to find the greatest common factor (GCF) of the number of carrots (90) and the number of leaves of lettuce (72). The GCF is the largest number that divides evenly into both numbers.
To find the GCF, we can use the prime factorization method:
Step 1: Prime factorize both numbers.
90 = 2 * 3^2 * 5
72 = 2^3 * 3^2
Step 2: Identify the common prime factors and their powers.
Both numbers have a common factor of 2 (with a power of 1) and 3 (with a power of 2).
Step 3: Multiply the common prime factors using the lowest power.
2^1 * 3^2 = 2 * 9 = 18
The GCF of 90 and 72 is 18. Therefore, the rabbit must have 18 baby bunnies in order to divide the carrots and leaves of lettuce evenly among them.
To find out how many baby bunnies the rabbit must have, we need to determine the greatest common factor (GCF) of 90 and 72. The GCF represents the largest number that divides evenly into both numbers.
Step 1: Find the factors of 90 and 72:
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
Step 2: Identify the common factors:
The common factors of 90 and 72 are 1, 2, 3, 6, 9, and 18.
Step 3: Determine the greatest common factor:
The greatest common factor (GCF) of 90 and 72 is 18.
Therefore, the rabbit must have 18 baby bunnies.