Glass panel

A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut?

Correct answer:

a =  24 cm
n =  12

Step-by-step explanation:

$$\begin{gathered} 72=2^3\cdot 3^2 \\ 96=2^5\cdot 3 \\ \text{GCD}(72,96)=2^3\cdot 3=24 \\ a=GCD(72,96)=24\text{ cm} \end{gathered}$$

$$\begin{gathered} S=72\cdot 96=6912{\text{cm}}^2 \\ {S}_2=a^2=24^2=576{\text{cm}}^2 \\ n=S\mathrm{/}{S}_2=6912\mathrm{/}576=12 \end{gathered}$$

Try another example

Related math problems and questions:

• Plumber
  The plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it?
• Largest squares
  How many of the largest square sheets did the plumber cut the honeycomb from 16 dm and 96 dm?
• Paper squares
  The paper rectangle measuring 69 cm and 46 cm should be cut into as many squares as possible. Calculate the lengths of squares and their number.
• Gcd and lcm
  Calculate the greatest common divisor and the least common multiple of numbers. a) 16 and 18 b) 24 and 22 c) 45 and 60 d) 36 and 30
• Cubes
  Carol with cut bar 12 cm x 12 cm x 135 cm to the cubes. Find the sum of all the surfaces of the resulting cubes.
• Square tiles
  The room has dimensions of 12 meters and 5.6 meters. Determine the number of square tiles and their largest dimension to exactly cover the floor.
• On Children's
  On Children's Day, the organizers bought 252 chewing gums, 396 candies and 108 lollipops. They want to make as many of the same packages as possible. Advise them what to put in each package and how many packages they can make this way.
• Pegs
  From two sticks 240 cm and 210 cm long, it is necessary to cut the longest possible pegs for flowers so that no residues remain. How many pegs will it be?
• Pexeso
  Drawing paper has dimensions of 60cm and 840mm. Pupils have to divide it into squares so that they can make a pexeso. What dimension must squares have if their side is to be larger than 3cm and less than 10cm?
• Sports students
  There are 120 athletes, 48 volleyball players, and 72 handball players at the school with extended sports training. Is it possible to divide sports students into groups so that the number in each group is the same and expressed by the largest possible num
• Tiles
  Hall has dimensions 325 &time; 170 dm. What is the largest size of square tiles that can be entire hall tiled, and how many we need them?
• Lcm = 22 + gcd
  The least common multiple of two numbers is 22 more than their greatest common divisor. Find these numbers.
• Gardens colony
  Gardens colony with dimensions of 180 m and 300 m are to be completely divided into the same large squares of the highest area. Calculate how many such squares can be obtained and determine the length of the square side.
• Decompose
  Decompose into primes and find the smallest common multiple n of (16,20) and the largest common divisor D of the pair of numbers (140,100)
• Square room
  What is the size of the smallest square room, which can pave with tiles with dimensions 55 cm and 45 cm? How many such tiles is needed?
• A rope
  A rope can be cut into equal length with no rope left over. The lengths can be 15cm,18cm or 25cm. What is the shortest possible length of the rope?
• The classroom
  The classroom is 9 meters long. The width of the classroom is smaller and can be passed in equally long steps of 55 CM or 70 CM. Determine the width of the classroom.