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.
The rabbit wants to give each bunny the same number of carrots and lettuce leaves. So the number of bunnies must be a factor of both the number of carrots (90) and the number of lettuce leaves (72).
Finding the common factors of 90 and 72:
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
From the lists above, the common factors are 1, 2, 3, 6, 9, 18.
Therefore, the rabbit must have either 1, 2, 3, 6, 9, or 18 baby bunnies in order to give each of them the same number of carrots and lettuce leaves.
To find out how many baby bunnies the rabbit must have, we need to determine the common divisor of 90 and 72. This common divisor will represent the number of carrots and leaves of lettuce each baby bunny will receive.
The prime factorization of 90 is 2 * 3^2 * 5, and the prime factorization of 72 is 2^3 * 3^2.
Therefore, the common divisor of 90 and 72 is 2 * 3^2, which is 18.
So, the rabbit must have 18 baby bunnies to give each of them the same number of carrots and leaves of lettuce.