Answer:
52 cm on a side
6 squares
Explanation:
The side length of each square will be the greatest common factor (GCF) of 104 cm and 156 cm.
Square size
Euclid's algorithm is useful for finding the GCF of two numbers whose factors you may not immediately know.
156/104 = 1 r 52 . . . . . . divide and keep the remainder
Replace the smaller number with the remainder and repeat:
104/52 = 2 r 0 . . . . . . . when the remainder is 0, the divisor is the GCF
The greatest common factor, and the side length of the square, is 52 cm.
Board size
In terms of the size of the square, the board is ...
104 cm / (52 cm) = 2 squares wide
156 cm / (52 cm) = 3 squares long
The number of squares that can be ruled on the board is 2×3 = 6.