# Greatest common divisor (GCD) - examples

1. A large A large gear will be used to turn a smaller gear. The large gear will make 75 revolutions per minute. The smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM. ]
2. 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,
3. 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?
4. Diofant 2 Is equation ? solvable on the set of integers Z?
5. 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?
6. Seedcake Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
7. 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)
8. 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?
9. 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?
10. Segments Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
11. 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?
12. 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
13. 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.
14. 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.
15. Self A math text book is 2 2/9 inches thick. how many of these books will fit on a 120-inch self?
16. Florist Florist has 84 red and 48 white roses. How many same bouquets can he make from them if he must use all roses?
17. 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?
18. 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
19. 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?
20. 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.

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