A rectangular cake measuring 120 cm by 72 cm is to be divided into square pieces of the same size and the largest size possible.What will be the measure of the side of each square and how many pieces will there be?

24 6 cm

(120*72)/(6*6) = 240

12 cm

(120*72)/(12*12) = 60

120cm and 72cm

GCF = 24

120/24=5
72/24=3

3X3=9 square pieces

To determine the size of each square and the number of pieces, we need to determine the greatest common divisor (GCD) of the length and width of the rectangular cake.

Step 1: Find the GCD using the Euclidean algorithm.
- Divide the larger dimension (120 cm) by the smaller dimension (72 cm): 120 ÷ 72 = 1 with a remainder of 48.
- Divide the smaller dimension (72 cm) by the remainder (48 cm): 72 ÷ 48 = 1 with a remainder of 24.
- Divide the remainder (48 cm) by the new remainder (24 cm): 48 ÷ 24 = 2 with no remainder.
- At this point, we have found the GCD, which is the remainder before the division by 0.
- Therefore, the GCD of 120 cm and 72 cm is 24 cm.

Step 2: Determine the size of each square.
- The GCD represents the side length that can divide the rectangular cake evenly.
- Hence, each square piece will have a side length of 24 cm.

Step 3: Calculate the number of square pieces.
- To find the number of pieces, divide the length of the rectangular cake by the side length of each square: 120 cm ÷ 24 cm = 5.
- Similarly, divide the width of the rectangular cake by the side length of each square: 72 cm ÷ 24 cm = 3.
- Multiply the two results together to obtain the total number of square pieces: 5 × 3 = 15.

Therefore, each square piece will have a side length of 24 cm, and there will be 15 pieces in total.