Question

greatest common factor - applications - item 51151
cesar has 32 boxes of pasta and 48 jars of sauce that he will be putting into bags for a food drive. he wants each bag to have the same amount of pasta and sauce and wants to use all of the items.
use the drop - down menus to complete the statements below about the number of bags cesar can make.
the greatest number of bags cesar can make is. each of these bags will have boxes of pasta and jars of sauce.
if he made fewer bags,.
he could use bags, but this is not the greatest number he could use.

Explanation:

Step1: Find GCF of 32 and 48

Factorize 32: \(32 = 2^5\)
Factorize 48: \(48 = 2^4 \times 3\)
GCF is \(2^4 = 16\). So max bags = 16.

Step2: Calculate items per bag

Pasta per bag: \(\frac{32}{16} = 2\)
Sauce per bag: \(\frac{48}{16} = 3\)

Step3: Fewer bags (e.g., 8, 4, 2, 1)

Fewer bags mean using a factor of 16 (less than 16). E.g., 8 bags: pasta \(32/8=4\), sauce \(48/8=6\) (more per bag).

Step4: Non - max bags (e.g., 8)

A non - max factor of 16 (like 8, 4, 2, 1). 8 is a factor (16÷2 = 8).

Answer:

The greatest number of bags Cesar can make is \(16\). Each of these bags will have \(2\) boxes of pasta and \(3\) jars of sauce.
If he made fewer bags, each bag would have more pasta and sauce (e.g., 8 bags: 4 pasta, 6 sauce).
He could use \(8\) (or 4, 2, 1) bags, but this is not the greatest number he could use.