Square gardens

The gardening colony with dimensions of 180 m and 300 m is to be completely divided into equally large square areas with the largest possible area. Calculate how many such square areas can be obtained and determine the side length of the square.

Correct answer:

a =  60 m
n =  15

Step-by-step explanation:

$$\begin{gathered} x=180\text{ m } \\ y=300\text{ m } \\ 180=2^2\cdot 3^2\cdot 5 \\ 300=2^2\cdot 3\cdot 5^2 \\ \text{GCD}(180,300)=2^2\cdot 3\cdot 5=60 \\ a=GCD(x,y)=GCD(180,300)=60\text{ m} \end{gathered}$$

$n=x\mathrm{/}a\cdot (y\mathrm{/}a)=180\mathrm{/}60\cdot (300\mathrm{/}60)=15$

Try another example

Related math problems and questions:

• 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.
• The land
  The land, which has dimensions of 220 m and 308 m, the owner wants to divide into equally large square plots with the largest possible area. How long will one side of the plot be?
• 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?
• Cutting paper
  Divide a rectangular paper with dimensions 220mm and 308mm into squares of the same size so that they are as large as possible. Specify the length of the side of the square.
• 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?
• 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.
• Largest squares
  How many of the largest square sheets did the plumber cut the honeycomb from 16 dm and 96 dm?
• 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?
• School books
  At the beginning of the school year, the teacher distributed 480 workbooks and 220 textbooks. How many pupils could have the most in the classroom?
• Two hundred
  Two hundred ten athletes competed in three athletics races on three fields. One hundred five athletes competed in the first, 60 in the second, and everyone else in the third. On the individual courts, the athletes were divided into groups. Each group, alt
• Reminder and quotient
  There are given the number C = 281, D = 201. Find the highest natural number S so that the C:S, D:S are with the remainder of 1,
• Tissues
  The store got three kinds of tissues - 132 children, 156 women and 204 men. Tissues each species were packed into boxes after the number of pieces the same for all three types (and greatest). Determine the number, if you know that every box has more than
• Wide field
  The field is 203 meters wide 319 meter long, what is the greater length of the rope by which length and width can be measured and find the exact number of time.
• Around the flowerbed
  Around a rectangular flowerbed with dimensions 5.25 m and 3.5 m are to be planted roses equally spaced so that the roses found in every corner of the flowerbed and consumed them as little as possible. a) At what distance are planted roses? b) How many ros
• Rectangular flowerbed
  Around the rectangular flowerbed with dimensions of 5.25 m and 3.50 m, roses should be planted at the same distance from each other so that the roses are located in each corner of the flower bed and are consumed as little as possible. How far do we plant
• 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.
• Bricks pyramid
  How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?