The local food bank is preparing take-home packages for people in need. They have 300 boxes of cereal, 550 cans of vegetables, and 480 bags of pasta. Find the greatest number of items that can be equally divided into take-home packages.(1 point)
Responses
30
30
25
25
20
20
10
10.
To find the greatest number of items that can be equally divided into take-home packages, we need to find the greatest common divisor (GCD) of the given quantities of cereal, vegetables, and pasta.
The GCD of 300, 550, and 480 is 10.
Therefore, the greatest number of items that can be equally divided into take-home packages is 10.
To find the greatest number of items that can be equally divided into take-home packages, we need to find the greatest common divisor (GCD) of the quantities of cereal, vegetables, and pasta.
First, let's determine the prime factors for each quantity:
300 boxes of cereal = 2^2 * 3 * 5^2
550 cans of vegetables = 2 * 5^2 * 11
480 bags of pasta = 2^5 * 3 * 5
To find the GCD, we need to find the smallest exponent for each prime factor that appears in all three quantities:
- The smallest exponent for 2 is 2.
- The smallest exponent for 3 is 1.
- The smallest exponent for 5 is 1.
- The smallest exponent for 11 is 0 (as it doesn't appear in the other quantities).
Therefore, the GCD is 2^2 * 3 * 5 = 20.
So, the greatest number of items that can be equally divided into take-home packages is 20.