Find the GCF of 78 and 86.(1 point) Responses 1 1 3 3 2 2 86
The GCF of 78 and 86 is 2.
What is the greatest common factor of 45 and 54?(1 point) Responses 45 45 1 1 9 9 3
The greatest common factor of 45 and 54 is 9.
Find the greatest common factor of 17 and 51.(1 point) Responses 3 3 51 51 17 17 1 1
The greatest common factor of 17 and 51 is 1.
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 3 3 9 9 18
To find the number of baby bunnies, we need to find the greatest common factor of 90 (carrots) and 72 (leaves of lettuce).
The prime factorization of 90 is 2 * 3^2 * 5, and the prime factorization of 72 is 2^3 * 3^2.
To find the greatest common factor, we take the smallest exponent for each prime factor. In this case, the exponent of 2 is 3 (from 72), the exponent of 3 is 2 (from both numbers), and the exponent of 5 is 0 (from 90).
So, the greatest common factor is 2^3 * 3^2, which is equal to 8 * 9 = 72.
Therefore, the rabbit must have 72 baby bunnies in order to distribute the carrots and leaves of lettuce evenly.
A carnival game gives variety bags as prizes. The game operator uses 100 balloons and 68 stickers to put into a certain number of bags. How many balloons and how many stickers can go in each bag if they make the greatest number of bags possible so that each bag has the same number of balloons and the same number of stickers?(1 point) Responses 17 balloons and 25 stickers 17 balloons and 25 stickers 50 balloons and 34 stickers 50 balloons and 34 stickers 4 balloons and 4 stickers 4 balloons and 4 stickers 25 balloons and 17 stickers
To find the greatest number of bags possible with the same number of balloons and stickers, we need to find the greatest common factor of 100 (balloons) and 68 (stickers).
The prime factorization of 100 is 2^2 * 5^2, and the prime factorization of 68 is 2^2 * 17.
To find the greatest common factor, we take the smallest exponent for each prime factor. In this case, the exponent of 2 is 2 (from both numbers) and the exponent of 5 and 17 is 0 (from 100 and 68, respectively).
So, the greatest common factor is 2^2, which is equal to 4.
Therefore, each bag can have 4 balloons and 4 stickers.