Question

Find the greatest number of identical first – aid kits that can make. Also, find the number of each first – aid kit contain if you have 48bandages,15squares of gauze,6tubes of antibiotic ointment andice packs.

Short answer

There will be three kits. In a kit there will be16 bandages,5 square gauze 2, tubes and2 packs of ice.

Step-by-step solution

Step -1 - Apply the concept of   Prime Factorization

In this, simply use the concept of Prime factorization of the numbers to get the greatest prime factor of the given numbers.

Step -2 – Find the Factorization to get the greatest common factor

Here,

The factors of 6 tubes of ointmentare:$1,2,3,6$

The factors of 6 ice packsare:$1,2,3,6$

The factors of 15 squares of gauzeare:$1,3,5,15$

The factors of48 bandagesare:$1,2,3,4,6,8,12,16,24,48$

Then the greatest common factor for the 4 items is3 .

So, from the above statement it conclude that a maximum of 3 identical kits could be made out of 48 bandages, 15 squares of gauze, 6 tubes of antibiotic and 6 ice packs.

Step -3 – Finding the number of items in each kit

Now, to find the number of items each kit will contain divide the total number of kits(i.e. GCF) with each number of items.

Now,

For Bandages, $\frac{Bandages}{Kits}=\frac{48}{3}=16bandages$

For Gauze, $\frac{Gauze}{Kits}=\frac{15}{3}=5gauze$

For Tubes,$\frac{Tubes}{Kits}=\frac{6}{3}=2tubes$

For Ice packs, $\frac{icepacks}{Kits}=\frac{6}{3}=2icepacks$

Therefore, in a kit there will be16 bandages,5 square gauze,2 tubes and packs of ice.