# 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.

Result

n =  15
c =  60 m

#### Solution:

$a=180 \ \text{m} \ \\ b=300 \ \text{m} \ \\ 180=2^2 \cdot 3^2 \cdot 5 \ \\ 300=2^2 \cdot 3 \cdot 5^2 \ \\ \text{GCD}(180, 300)=2^2 \cdot 3 \cdot 5=60 \ \\ \ \\ c=GCD(180, 300)=60 \ \text{m} \ \\ S=a \cdot \ b=180 \cdot \ 300=54000 \ \text{m}^2 \ \\ S_{1}=c^2=60^2=3600 \ \text{m}^2 \ \\ n=S/S_{1}=54000/3600=15$
$c=60 \ \text{m}$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Do you want to calculate greatest common divisor two or more numbers?
Do you want to convert area units?
Do you want to convert length units?

## Next similar math problems:

1. Argicultural field
Field has a rectangular shape with a width 180 m and circumference 940 m. How many hectares acreage has field?
2. Square glass
What is the area of the square window glass with the side 4 dm? Do you know how many cm2 is it?
3. Rainfall
How many liters of water did fell in a 32m long and 8m wide garden, if 8mm of rain fell?
4. Area of rectangle
Calculate the area of rectangle in square meters whose sides have dimensions a = 80dm and b = 160dm.
5. Tiles
How many 46 cm square tiles will cover a floor 22.08 m by 8.74 m?
6. Apartment area
Anton wanted to measure the area of the apartment. But he bought a meter only 1.5m long. Later he recalled that he had two meters long at 4.5m and 18m at home. How many times are home gauges longer than the meter he bought?
7. Divisibility
Determine all divisors of number 84.
8. Digit sum
Determine for how many integers greater than 900 and less than 1,001 has digit sum digit of the digit sum number 1.
9. Steps
Walkway from the house to the school is 180 m long. How many more steps Michael makes than his father on the way to school, if the length of Michael's step is 60 cm and the length of his father's step is 90 cm.
10. Divisibility 2
How many divisors has integer number 13?
11. Rectangles
Calculate how many squares/rectangles of size 4×3 cm can be cut from a sheet of paper of 36 cm × 32 cm?
12. Rape
The agricultural cooperative harvested 525 ares of rape, of which received 5.6 tons of rape seeds. Calculate the yield per hectare of rape.
13. Area
Calculate: ?
14. Land
Land has a rectangular shape, its surface area is 1.45 hectares. Its width is 250 m. Determine the length of the land.
15. One hectare
How many square meters are one hectare?
16. Bathroom 2
A bathroom is 2.4 meters long and 1.8 meters wide. How many square tiles 1 dm on each side are to be used to cover it?
17. Write decimals
Write in the decimal system the short and advanced form of these numbers: a) four thousand seventy-nine b) five hundred and one thousand six hundred and ten c) nine million twenty-six