Huxian needs to pack 171 pens 63pencils and 27 erasers into identical gift bags so that each item is equally distributed among the gift bags find the number of each item in a gift bag

number of pens in each bag: 19

number of pencils in each bag: 7

number of erasers in each bag: 3

Step-by-step explanation:

To find how many pens, pencils and erasers Huxian needs to put in each gift bag, we need to calculate the greatest common divisor (gcd) of 171, 63 and 27. We can do that decomposing each number in their prime divisors, and then we multiply the common values:

decomposing 171: 3*3*19

decomposing 63: 3*3*7

decomposing 27: 3*3*3

The common values are 3 and 3, and the product of these values indicate the number of bags that will be formed:

number of bags = 3*3 = 9

Then, the remaining values of each one will be the number of each element put into each bag:

number of pens in each bag: 19

number of pencils in each bag: 7

number of erasers in each bag: 3