there are 20 red pencils and 24 green pencils how can we distribute them equally in box?largest number of pencil for a box

Question

I want to know the largest number of pencils which can be put in each box ?

Answer 1

It looks like what you are asking is how we can make identical boxes of pencils, with as many pencils as possible in each box. This probably isn't the real question, though. I will answer it first, then suggest a different question.

 

If we have just one box, it will have 44 pencils, and that is the largest number of pencils we can have.

 

If we have two boxes, then we can put 10 red and 12 green pencils in it, so we'd have 22 pencils in each box. I think you can see why I don't think that is really the question.

 

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What I think the question really is, is "What is the greatest number of boxes of pencils we can make, with the same number of red and green pencils in each box?"

 

This is a GCF (greatest common factor) problem. What is the greatest number that will evenly divide into both 20 and 24? Well, 2 will go into both of them evenly, but is there anything greater than 2 that will? Yes, 4 will.

 

Now, is there anything more than 4 that will go into both 20 and 24 evenly? No, there isn't, so 4 is the GCF.

 

***** Side note:

The rigorous way to find the GCF is to factor each number into prime factors.

20 = 2x2x5            24 = 2x2x2x3

The next step is easiest if you put the prime factors in increasing order, as I have done.

 

Now, looking at the lists of factors, what do they have in common?

I see two 2s in both lists, but nothing more than that, so the GCF is two 2s, which is 2x2 = 4.

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This tells us that the most boxes we can have with the same number of each color in it is 4 boxes.

 

20/4 = 5, so there will be 5 red pencils in each box.

 

24/4 = 6, so there will be 6 green pencils in each box.

 

So, if we want the maximum number of identical boxes, we would have 4 boxes with 5 red and 6 green pencils in each box.