Question

A rectangular board is 104cm wide and 156. cm long Equal squares, os large as possible,are ruled of this board find the size of the squares, how many squares are there?​

Answer 1

Answer:

  52 cm on a side

  6 squares

Step-by-step 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.