As all of the bundles have the same content inside, so assuming that there is x number of Fiction books and y number of Non-fiction books in each bundle.
Let n be the total number of bundles that my team can send.
There are 64 Fiction books, so
nx=64 ...(i)
Or x=64/n ...(ii)
also, there are 48 Non-Fiction books, so
ny=48 ...(iii)
Or y=48/n ...(iv)
Observing that the numbers x, y, and n are counting numbers and from equations (i) and (iii), n is the common factor of 64 and 48.
The possible common factors of 64 and 48 are,
n=1,2,4,8, and 16.
So, my team can send 1,2,3,4,8 or 16 bundles of books.
Now, from equations (ii) and (iv),
For n=1:
x=64/1=64
y=48/1=48
So, for 1 bundle the number of Fiction and Non-fictions books are 64 and 48 respectively.
For n=2:
x=64/2=32
y=48/2=48
So, for 2 bundles, the number of Fiction and Non-fictions books are 32 and 24 respectively.
For n=4:
x=64/4=16
y=48/4=12
So, for 4 bundles, the number of Fiction and Non-fictions books are 16 and 12 respectively.
For n=8:
x=64/8=8
y=48/8=6
So, for 8 bundles, the number of Fiction and Non-fictions books are 8 and 6 respectively.
For n=16:
x=64/16=4
y=48/16=3
So, for 16 bundles, the number of Fiction and Non-fictions books are 4 and 3 respectively.
√25