Rafael wishes to cut some identical squares from a vanguard sheet measuring 72cm in length and 45 cm in breath. He wants each square to be as big as possible, and with no left over van guard sheet. What is the length of each square? and what is the total number of such squares that can be cut from the vanguard sheet?.

TIA

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Assumming they are looking for whole number

Look for the highest common factor 72 and 45

Start from least number of factors, i.e 45, only 4 of them below,

Factors for 45

3 X 15

9 X 5

Check if 3,5,9 and 15 are among the factors for 72. Just use calculator and key in one by one.

3 X 24

8, X 9

A 9 X 9 squares would work nicely. ## 81 cm^{2} of area

Look at the corresponding blue number, the product is the number of squares in the vanguard.

5 X 8 = 40 squares ###

The largest common factor between 45 and 72 is 9.

Hence the length of each square is **9cm**.

Number of squares that can be cut from the breadth is 45/9 = 5

Number of squares that can be cut from the length is 72/9 = 8

Hence total number of squares is 8×5 = **40**.

Check that 9x9x40 = 72×45 = 3240 cm^{2}

Note that if the question asks for the *smallest* possible square, then you should be looking for the smallest common factor between 45 and 72, which would be 3.