Peter has 48 gold coins and 32 silver coins. he wants to put them into as many boxes as possible. the number of gold coins and silver coins are to be divided equally among the boxes. how many boxes does he need

To find the biggest number of boxes needed, you need to find the highest common factor for both of 48 and 32

Finding the highest common factor:
48 = 2^4 x 3
32 = 2^5
Take the number that has a common base and lowest index from both of them:
2^4
= 16

Since 16 is the highest common factor of both of them, he will need 16 boxes at most (3 gold coins and 2 silver coins in each)