# Greatest common divisor (GCD) - problems

- Trees in alley

There are four trees in the alley between which the distances are 35m, 15m and 95m. Trees must be laid in the spaces so that the distance is the same and the maximum. How many trees will they put in and what will be the distance between them? - Hectares

The tractor plows the first day of 4.5ha, the second day 6.3ha and the third day 5.4ha. It worked whole hours a day, and its hourly performance did not change and was the highest of the possible. How many hectares did it plow in one hour (what is it perfor - MO C–I–1 2018

An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones. - Birthdate

Jane on birthday brought 30 lollipops and 24 chewing gum for their friends. How many friends has, if everyone receives the same number of lollipops and chewing gums? How much chewing gum and lollipops got any friend? - Diofant 2

Is equation ? solvable on the set of integers Z? - Plumber

Plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares so that no waste. Calculate the length of the sides of a square. How many squares cut it? - Seedcake

Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros? - Diofant equation

In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions) - 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? - School books

At the beginning of the school year, the teacher gave out 480 books and 220 textbooks. How many students were in the class? - 9.A

9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5? - Segments

Line segments 67 cm and 3.1 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide? - 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 - 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 12 meters and 5.6 meters. Determine the number of square tiles and their largest dimension to exactly cover the floor. - Self

A math text book is 2 2/9 inches thick. how many of these books will fit on a 120-inch self? - Florist

Florist has 84 red and 48 white roses. How many same bouquets can he make from them if he must use all roses? - Apples and pears

Mom divided 24 apples and 15 pears to children. Each child received the same number of apples and pears - same number as his siblings. How many apples (j=?) and pears (h=?) received each child? - 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 6 - Shepherd

The shepherd has fewer than 500 sheep; where they can be up to 2, 3, 4, 5, 6 row is always 1 remain, and as can be increased up to 7 rows of the sheep, and it is not increased no ovine. How many sheep has a shepherd?

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