Mia needs to separate 270 blue pens and 180 red pens into packs. each pack will have the same number of blue pens and the same number of red pens. what is the greatest number of packs she can make? how many red pens and blue pens will be in each pack?

Hello there!

in this case, we need we want to divide 270 blue pens and 180 red pens into packs. And each pack has the same amount of red pens and blue pens.

We want to find the maximal common factor between these numbers:

A way of doing this is seeing the divisors of the smaller number, and see if this divisor also divide the bigger number.

The biggest divisor of 180 (different than the same number) is 90 because of 180/2 = 90, and 180/90 = 2

let's see if 90 also divides 270.

270/90 = 3  

ok, so 90 is a common factor of both numbers, this means that the maximum amount of packs possible is 90 packs

Now the number of pens of each color in the pack is equal to the quotient between the total number of pens of each color and the number of packs.

So we can divide the pens into 90 packs, where each bag has 2 red pens and 3 blue pens.

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step-by-step explanation: